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Abstract The similarity test of ship stiffened plate structures under underwater explosions is a cost-effective and efficient method to evaluate the vitality of ships and guide the design of their shock resistance. This study focuses on the nonlinear impact response model tests of ship stiffened plate structures and their similarity laws with actual ships. The vertical motion of the ship stiffened plate structure is characterized by the Hurst index, and an equivalent relationship between the Hurst index of the model and the prototype is derived from classical similarity law. Based on the Hurst index, a similarity transformation relationship between the strain signals of the model and prototype is established. To verify the conclusions, similarity experiments of underwater explosions were conducted on both the model and the prototype. The original signals were grouped by the natural vibration period to determine the variation of the Hurst index over time. The model experiment strain signals for each natural vibration period were converted and compared with the prototype experiment results to verify the method's effectiveness. Simultaneously, the Hurst index of the stiffened plate structure under explosive shock load and its similarity transformation relationship with the prototype were simulated and analyzed. This provides theoretical and technical support for conducting analogous nonlinear response experiments for ship underwater explosions.

Abstract Background The key role of thrombospondin 1 (THBS1) in the pathogenesis of acute-on-chronic liver failure (ACLF) is unclear. Here, we present a transcriptome approach to evaluate THBS1 as a potential biomarker in ACLF disease pathogenesis. Methods Biobanked peripheral blood mononuclear cells (PBMCs) from 330 subjects with hepatitis B virus (HBV)-related etiologies, including HBV-ACLF, liver cirrhosis (LC), and chronic hepatitis B (CHB), and normal controls (NC) randomly selected from the Chinese Group on the Study of Severe Hepatitis B (COSSH) prospective multicenter cohort underwent transcriptome analyses (ACLF = 20; LC = 10; CHB = 10; NC = 15); the findings were externally validated in participants from COSSH cohort, an ACLF rat model and hepatocyte-specific THBS1 knockout mice. Results THBS1 was the top significantly differentially expressed gene in the PBMC transcriptome, with the most significant upregulation in ACLF, and quantitative polymerase chain reaction (ACLF = 110; LC = 60; CHB = 60; NC = 45) was used to verify that THBS1 expression corresponded to ACLF disease severity outcome, including inflammation and hepatocellular apoptosis. THBS1 showed good predictive ability for ACLF short-term mortality, with an area under the receiver operating characteristic curve (AUROC) of 0.8438 and 0.7778 at 28 and 90 days, respectively. Enzyme-linked immunosorbent assay validation of the plasma THBS1 using an expanded COSSH cohort subjects (ACLF = 198; LC = 50; CHB = 50; NC = 50) showed significant correlation between THBS1 with ALT and γ-GT (P = 0.01), and offered a similarly good prognostication predictive ability (AUROC = 0.7445 and 0.7175) at 28 and 90 days, respectively. ACLF patients with high-risk short-term mortality were identified based on plasma THBS1 optimal cut-off value (

Developing functional ductal organoids (FDOs) is essential for liver regenerative medicine. We aimed to construct FDOs with biliary tree networks in rat decellularized liver scaffolds (DLSs) with primary cholangiocytes isolated from mouse bile ducts. The developed FDOs were dynamically characterized by functional assays and metabolomics for bioprocess clarification. FDOs were reconstructed in DLSs retaining native structure and bioactive factors with mouse primary cholangiocytes expressing enriched biomarkers. Morphological assessment showed that biliary tree-like structures gradually formed from day 3 to day 14. The cholangiocytes in FDOs maintained high viability and expressed 11 specific biomarkers. Basal-apical polarity was observed at day 14 with immunostaining for E-cadherin and acetylated α-tubulin. The rhodamine 123 transport assay and active collection of cholyl-lysyl-fluorescein exhibited the specific functions of bile secretion and transportation at day 14 compared to those in monolayer and hydrogel culture systems. The metabolomics analysis with 1075 peak pairs showed that serotonin, as a key molecule of the tryptophan metabolism pathway linked to biliary tree reconstruction, was specifically expressed in FDOs during the whole period of culture. Such FDOs with biliary tree networks and serotonin expression may be applied for disease modeling and drug screening, which paves the way for future clinical therapeutic applications.

The main purpose of this research was to use wood as a core material of composite sandwiched submersible pressure hulls to reduce weight and increase stability under hydrostatic pressure. This task presents design optimization for a submersible pressure hull by means of Finite Element Analysis (FEA). Different composite materials were implemented, and various kinds of woods were consumed as a core. Genetic Algorithm (GA) was used to conduct the optimization process. The ply layer numbers and core thickness, for pressure hulls have been optimized for the configuration of [0l/90m/0n/0c/0o/90p/0q]. The objective function was to decrease the buoyancy factor and to increase the buckling factor. The material failure criteria, and buckling factor were selected as constraints for the optimization process. A comparison was made between the steel pressure hull and promising results were achieved comparatively in favor of using composite material with the combination of wood core.

Abstract Background The pathophysiology of hepatitis B-related liver cirrhosis (HBV-LC) remains unclear. This study aimed to explore the disease mechanisms using topological analysis of the miRNA/mRNA network. Methods Paired miRNA/mRNA sequencing was performed with thirty-three peripheral blood mononuclear cell samples (LC, n = 9; chronic hepatitis B, n = 12; normal controls, n = 12) collected from a prospective cohort to identify the miRNA/mRNA network. Topological features and functional implications of the network were analyzed to capture pathophysiologically important miRNAs/mRNAs, whose expression patterns were confirmed in the validation group (LC, n = 15; chronic hepatitis B, n = 15; normal controls, n = 10), and functional potentials initiating fibrogenesis were demonstrated in vitro. Results The miRNA/mRNA network contained 3121 interactions between 158 differentially expressed (DE) miRNAs and 442 DE-mRNAs. The topological analysis identified a core module containing 99 miRNA/mRNA interactions and two hub nodes (miR-20a-5p/miR-340-5p), which connected to 75 DE-mRNAs. The expression pattern along the disease progression of the core module was found associated with a continuous increase in wound healing, inflammation, and leukocyte migration but an inflection of immune response and lipid metabolic regulation, consistent with the pathophysiology of HBV-LC. MiR-20a-5p/miR-340-5p were found involved in macrophage polarization and hepatic stellate cell (HSC) activation in vitro (THP-1, LX-2 cell lines), and their expression levels were confirmed in the validation group independently. Conclusion Topological analysis of the miRNA/mRNA network in HBV-LC revealed the association between fibrosis and miR-20a-5p/miR-340-5p involving initiating activations of macrophage and HSC. Further validations should be performed to confirm the HSC/macrophage activations and the interactions between miR-20a-5p/miR-340-5p and their potential targets, which may help to develop non-invasive prognostic markers or intervention targets for HBV-LC.

Abstract To explore the cushioning properties of expanded polystyrene (EPS), a novel two‐degree‐of‐freedom mathematical model is proposed with a dynamic nonlinear system and successfully implemented it. The maximum response acceleration of the product was first determined in the novel dynamic mathematical model and used as a parameter for evaluating product damage. Furthermore, a drop test was carried out to verify the theoretical model and showed good consistency. Based on the correct theoretical model, a number of simulations with different drop heights and thicknesses of the cushion were done to investigate cushioning properties of EPS. The results show that EPS can reduce the maximum response acceleration of the product by more than 20% of the excitation acceleration. Thus, EPS has good cushioning ability and can be used as packaging material to protect products. Finally, the theoretical model was applied to an example application. A new method for constructing the cushioning curve is recommended, which could replace the traditional ASTM D 1596 drop test method.

Background & Aims: HBV-related acute-on-chronic liver failure (HBV-ACLF) is a complex syndrome associated with high short-term mortality. This study aims to reveal the molecular basis and identify novel HBV-ACLF biomarkers. Methods: Seventy patients with HBV-ACLF and different short-term (28 days) outcomes underwent transcriptome sequencing using peripheral blood mononuclear cells. Candidate biomarkers were confirmed in two external cohorts using ELISA. Results: Cellular composition analysis with peripheral blood mononuclear cell transcriptomics showed that the proportions of monocytes, T cells and natural killer cells were significantly correlated with 28-day mortality. Significant metabolic dysregulation of carbohydrate, energy and amino acid metabolism was observed in ACLF non-survivors. V-set and immunoglobulin domain-containing 4 (VSIG4) was the most robust predictor of patient survival (adjusted p = 1.74 × 10−16; variable importance in the projection = 1.21; AUROC = 0.89) and was significantly correlated with pathways involved in the progression of ACLF, including inflammation, oxidative phosphorylation, tricarboxylic acid cycle and T-cell activation/differentiation. Plasma VSIG4 analysis externally validated its diagnostic value in ACLF (compared with chronic liver disease and healthy groups, AUROC = 0.983). The prognostic performance for 28-/90-day mortality (AUROCs = 0.769/0.767) was comparable to that of three commonly used scores (COSSH-ACLFs, 0.867/0.884; CLIF-C ACLFs, 0.840/0.835; MELD-Na, 0.710/0.737). Plasma VSIG4 level, as an independent predictor, could be used to improve the prognostic performance of clinical scores. Risk stratification based on VSIG4 expression levels (>122 μg/ml) identified patients with ACLF at a high risk of death. The generality of VSIG4 in other etiologies was validated. Conclusions: This study reveals that immune-metabolism disorder underlies poor ACLF outcomes. VSIG4 may be helpful as a diagnostic and prognostic biomarker in clinical practice. Impact and implications: Acute-on-chronic liver failure (ACLF) is a lethal clinical syndrome associated with high mortality. We found significant immune cell alterations and metabolic dysregulation that were linked to high mortality in patients with HBV-ACLF based on transcriptomics using peripheral blood mononuclear cells. We identified VSIG4 (V-set and immunoglobulin domain-containing 4) as a diagnostic and prognostic biomarker in ACLF, which could specifically identify patients with ACLF at a high risk of death.

Abstract Background Sepsis is defined as a systemic inflammatory response to microbial infections with multiple organ dysfunction. This study analysed untargeted metabolomics combined with proteomics of serum from patients with sepsis to reveal the underlying pathological mechanisms involved in sepsis. Methods A total of 63 patients with sepsis and 43 normal controls were enrolled from a prospective multicentre cohort. The biological functions of the metabolome were assessed by coexpression network analysis. A molecular network based on metabolomics and proteomics data was constructed to investigate the key molecules. Results Untargeted metabolomics analysis revealed widespread dysregulation of amino acid metabolism, which regulates inflammation and immunity, in patients with sepsis. Seventy-three differentially expressed metabolites (|log2 fold change| > 1.5, adjusted P value 1.5) that could predict sepsis were identified. External validation of the hub metabolites was consistent with the derivation results (area under the receiver operating characteristic curve (AUROC): 0.81–0.96/0.62–1.00). The pentose phosphate pathway was found to be related to sepsis-associated encephalopathy. Phenylalanine metabolism was associated with sepsis-associated acute kidney injury. The key molecular alterations of the multiomics network in sepsis compared to normal controls implicate acute inflammatory response, platelet degranulation, myeloid cell activation involved in immune response and phenylalanine, tyrosine and tryptophan biosynthesis, and arginine biosynthesis. Conclusions Integrated analysis of untargeted metabolomics and proteomics revealed characteristic metabolite and protein alterations in sepsis, which were mainly involved in inflammation-related pathways and amino acid metabolism. This study depicted the pathological characteristics and pathways involved in sepsis and potential therapeutic targets.

Summary: Background: Liver transplantation (LT) is an effective therapy for acute-on-chronic liver failure (ACLF) but is limited by organ shortages. We aimed to identify an appropriate score for predicting the survival benefit of LT in HBV-related ACLF patients. Methods: Hospitalized patients with acute deterioration of HBV-related chronic liver disease (n = 4577) from the Chinese Group on the Study of Severe Hepatitis B (COSSH) open cohort were enrolled to evaluate the performance of five commonly used scores for predicting the prognosis and transplant survival benefit. The survival benefit rate was calculated to reflect the extended rate of the expected lifetime with vs. without LT. Findings: In total, 368 HBV-ACLF patients received LT. They showed significantly higher 1-year survival than those on the waitlist in both the entire HBV-ACLF cohort (77.2%/52.3%, p 10. These results were prospectively validated. Interpretation: COSSH-ACLF IIs identified the risk of death on the waitlist and accurately predicted post-LT mortality and survival benefit for HBV-ACLF. Patients with COSSH-ACLF IIs 7–10 derived a higher net survival benefit from LT. Funding: This study was supported by the National Natural Science Foundation of China (No. 81830073, No. 81771196) and the National Special Support Program for High-Level Personnel Recruitment (Ten-thousand Talents Program).

Background Immune-checkpoint inhibitors (ICIs) remain ineffective in a large group of non-small cell lung cancer (NSCLC) patients. Mucosal-associated invariant T (MAIT) cells, a population of unconventional innate-like T lymphocytes abundant in the human body, play important roles in human malignancies. Little is known about the immune characteristics of MAIT cells in NSCLC and correlation with prognosis and response rate of ICIs treatment.Methods To investigate the distribution, activation status, and function of MAIT cells in NSCLC patients and their correlations with anti-PD-1 immunotherapy, MAIT cells in peripheral blood, tumor and paratumor samples from NSCLC patients with or without anti-PD-1 immunotherapy were analyzed using flow cytometry and single-cell RNA-sequencing.Results MAIT cells were enriched in the tumor lesions of NSCLC patients migrating from peripheral blood via the CCR6-CCL20 axis. Both peripheral and tumor-infiltrating MAIT cells displayed an exhausted phenotype with upregulated PD-1, TIM-3, and IL-17A while less IFN-γ. Anti-PD-1 therapy reversed the function of circulating MAIT cells with higher expression of IFN-γ and granzyme B. Subcluster MAIT-17s (defined as cells highly expressing exhausted and Th17-related genes) mainly infiltrated in the non-responsive tissues, while the subcluster MAIT-IFNGRs (cells expressing genes related to cytotoxic function) were mainly enriched in responsive tissues. Moreover, we found predictive value of circulating MAIT cells for anti-PD-1 immunotherapy in NSCLC patients.Conclusions MAIT cells shifted to an exhausted tumor-promoting phenotype in NSCLC patients and the circulating MAIT subset could be a predictor for patients who respond to anti-PD-1 immunotherapy.

This paper describes a design optimization study of the composite egg-shaped submersible pressure hull employing optimization and finite element analysis (FEA) tools as a first attempt to provide an optimized design of the composite egg-shaped pressure hull for manufacturing or further investigations. A total of 15 optimal designs for the composite egg-shaped pressure hull under hydrostatic pressure are obtained in terms of fibers’ angles and the number of layers for 5 lay-up arrangements and 3 unidirectional (UD) composite materials. The optimization process is performed utilizing a genetic algorithm and FEA in ANSYS. The minimization of the buoyancy factor (B.F) is selected as the objective for the optimization under constraints on both material failure and buckling strength. Nonlinear buckling analysis is conducted for one optimal design considering both geometric nonlinearity and imperfections. A sensitivity study is also conducted to further investigate the influence of the design variables on the optimal design of the egg-shaped pressure hull.

The main objective of this study is to design composite shells i.e. long, short, thin and thick for the different underwater applications. These shells can be a part of pressure hulls, underwater vehicles, pressurized tanks, underwater cables and underwater pipelines etc. This paper presents comprehensive procedures for the mathematical modeling of elastic buckling for submersible composite shells under hydrostatic pressure. First order shear deformation theory (FOSDT) was used for modeling. FOSDT theory was mathematically derived under hydrostatic pressure for composite shells, and it can be used for all types of submersible shells. After the derivation of the theory, mathematical code was formed on MATLAB for this modeling. From the given formulation one can design the shell structure according to his needs on different environment conditions. Different types of composite shells, including moderately thick, thick, long, and short, are investigated for the FOSDT formulation to check the accuracy range. The results were compared with previous studies and finite element analysis FEA. Three types of materials, Carbon/Epoxy, Glass/Epoxy, and Boron/Epoxy, were used with different cross-ply symmetric and unsymmetrical angle configurations. The layups used for the analysis were [0/90/0]s [90/0/90/0]s [02/902]s [90/02/90]s [0/902/0]s [0/0/0/90]s [90/90/90/0]s and [0/90].

This paper is aimed at proposing a new approach to Reliability-based Design Optimization (RBDO) and applying it to cushioning packaging design with a highly nonlinear system. The problem is formulated as an RBDO problem, which is included a minimizing cost function and probabilistic constraints. Here, the thickness of the cushion material is dealt with uncertainty and uncontrolled parameters. The traditional reliability index approach (RIA) has evolved as a powerful tool to solve the RBDO problem; however, due to its convergence problem, the modified reliability index approach (MRIA) is proposed. Although the MRIA method solves the problems of the traditional RIA, it inherits the low efficiency of searching for the most probability point (MPP). Thus, we developed a novel RIA based on MRIA to improve the efficiency and robustness during the RBDO process. The innovation active set strategy is developed in reliability assessment, which is a strict inequality to determine whether the current constraint is active or inactive. An application example is presented, and the results are compared with MRIA to assess cost-effectiveness and efficiency. Results indicate the proposed method is feasible to solve the uncertainty problem of packaging materials in the processing process and is also an efficient RBDO method.

Stress field analysis is an essential part of umbilical component layout design. The stress field analysis of an umbilical, via numerical simulation, has commonly been applied in practical engineering. The high economic and time cost associated with numerical simulation and analysis of the stress field in an umbilical has been replaced by data-driven, deep-learning-based, real-time computational methods. In this study, a novel Pyramidal Efficient U-Net (PyEf-U-Net) network is proposed to predict the stress field distribution of the umbilical. The input dataset is obtained via the Differential Evolution-Generalized Lagrange Multiplier (DE-GLM) method, which is entered into the network for training, with a detailed discussion of the effects of hyperparameters such as optimizer, learning rate, and loss function on the performance of the network. The experimental research demonstrates that the proposed PyEf-U-Net can accurately predict the stress field of the umbilical in real time with a prediction accuracy of 94.2%, which is superior to other deep learning networks. The proposed method can provide an effective way for rapid mechanical analysis and design of the umbilical in practical engineering, while the method can be extended to the mechanical analysis and design of other similar marine engineering equipment structures.

This paper presents the design optimization of composite submersible cylindrical pressure hull subjected to 3 MPa hydrostatic pressure. The design optimization study is conducted for cross-ply layups [0s/90t/0u], [0s/90t/0u]s, [0s/90t]s and [90s/0t]s considering three uni-directional composites, i.e. Carbon/Epoxy, Glass/Epoxy, and Boron/Epoxy. The optimization study is performed by coupling a Multi-Objective Genetic Algorithm (MOGA) and Analytical Analysis. Minimizing the buoyancy factor and maximizing the buckling load factor are considered as the objectives of the optimization study. The objectives of the optimization are achieved under constraints on the Tsai-Wu, Tsai-Hill and Maximum Stress composite failure criteria and on buckling load factor. To verify the optimization approach, optimization of one particular layup configuration is also conducted in ANSYS with the same objectives and constraints.

To further investigate and improve the cleaning ability of the cavitation nozzle, this paper proposes a new model that is based on the Helmholtz nozzle and with the quadratic equation curve as the outer contour of the cavitation chamber. First, the numerical simulation of the flow field in the nozzle chamber was conducted using FLUENT software to analyze and compare the impact of the curve parameters and Reynolds number on the cleaning effect. Next, the flow field was captured by a high-speed camera in order to study the cavitation cycle and evolution process. Then, experiments were performed to compare the cleaning effect of the new nozzle with that of the Helmholtz nozzle. The study results demonstrate that effective cavitation does not occur when the diameter of the cavitation chamber is too large. For the new nozzle, with the increase of the Reynolds number, the degree of cavitation in the chamber first increases and then decreases; the cleaning effect is much better than that of a traditional Helmholtz nozzle under the same conditions; the nozzle has the best cleaning effect for the stand-off distance of 300 mm. HIGHLIGHTS A new type of cavitation nozzle based on the one-dimensional quadratic equation curve.; Through the orthogonalization experiment the optimal solution was obtained.; Explore the cavitation period and the change of bubble diameter and liquid volume fraction.; Explore the cleaning target distance and cleaning effect.; Verify the performance of new nozzles and traditional nozzles through experiments.;

To improve the evaluation efficiency of failure probability in RBDO models with uncertainty, many RIA-based, PMA-based methods have evolved as a powerful procedure, including the modified reliability index approach (MRIA), PMA two-level, PMA with sequential approximate programming (SAP). However, MRIA may encounter inefficiency and instability when applied to complex concave performance functions, and so does PMA two-level, not for PMA with SAP. The active set strategy-based SAP (ASS-based SAP) for PMA is proposed to accelerate computational efficiency through establishing an active set strategy and a deciding factor. The active set strategy defined by using inequality is to identify the feasible most probable target point (MPTP) in the inner loop. The decision factor integrates the reliability index and the active set strategy to quickly renew the active constraints in the outer loop. The reliability assessment and outer optimization are driven simultaneously, thereby the computational efficiency is strengthened. Numerical examples are compared with other reliability methods to demonstrate the excellent performance of the proposed method in efficiency and robustness. Results also show that the proposed method has the ability to solve complex RBDO problems.

ABSTRACT The genus Nocardia includes ubiquitous environmental saprophytes and the most frequently isolated aerobic actinomycete human pathogen responsible for localized or disseminated infection. Herein, the species distribution and antimicrobial susceptibility profiles of 441 nonrepetitive Nocardia strains are reported, collected from 21 provinces/cities in China over 13 years (from 2009 to 2021). These isolates were identified to species level by mass spectrometry or targeted DNA sequencing. The susceptibility profiles of Nocardia species for 15 antibiotics were determined by the broth microdilution method. Among these Nocardia isolates, Nocardia farcinica was the most commonly isolated species (39.9%, 176 of 441), followed by Nocardia cyriacigeorgica (28.6%, 126), Nocardia abscessus (6.6%, 29), and Nocardia otitidiscaviarum (5.9%, 26). Furthermore, 361 Nocardia strains (81.9%) were collected from lower respiratory tract (sputum, lung tissue, and bronchoalveolar lavage fluid), 50 (11.3%) were collected from skin and soft tissues, 9 were collected from blood, 9 were collected from eye, 4 were collected from cerebrospinal fluid and brain abscesses, and 2 were collected from pleural effusion. All of the Nocardia strains were susceptible to linezolid, followed by amikacin (99.3%) and trimethoprim-sulfamethoxazole (TMP-SMX) (99.1%). The antibiotic resistance profiles of other antibiotics varied tremendously among different Nocardia species. This demonstrated that accurate species identification and/or antibiotic susceptibility testing should be performed before the usage of these antibiotics. In summary, this is the largest study on the species and antibiotic resistance profiles of the genus Nocardia circulating in China, and our data will contribute to a better understanding of clinical nocardiosis. IMPORTANCE The genus Nocardia has the potential to cause nocardiosis, which might be underrecognized and underdiagnosed. Herein, the demographical features of 441 nonrepetitive nocardiosis cases and species distribution of their Nocardia strains in China, 2009 to 2021, are summarized. The susceptibility profiles for 15 antibiotics against all of the above Nocardia strains were also determined by the broth microdilution method. To date, this is the largest study on the genus Nocardia contributing to nocardiosis in China. Our study will be helpful for understanding the species diversity of Nocardia isolates distributed in China and for decision-making in the context of nocardiosis diagnosis and treatment.

Self-excited oscillating pulsed cavitation jet has many advantages, such as easy operation, simply maintenance, and low investment costs. Based on the structural parameters of the traditional Helmholtz and organ pipe single-chamber self-excited oscillating pulsed nozzles, Helmholtz + Helmholtz, organ pipe + organ pipe, and Helmholtz + organ pipe dual-chamber self-excited oscillating pulsed nozzles with different structures are established in series, and the internal flow field of the dual chamber is studied to obtain the best combination nozzle by comparing numerical simulation and erosion experiments. The results indicate that the cleaning effect is the best when adopting the combined structure of Helmholtz + organ pipe, which brings out the largest volume fraction of the nozzle cavity with higher gas content and higher kinetic energy with larger jet velocity. By comparing the erosion experiments, it is found that the flushing area and erosion depth of the nozzle with the ratio of cavity and wall (D/a) of 2.50 is significantly higher than the nozzle with the ratio of cavity and wall (D/a) of 5.00. The pulse pressure of the flushing target increases by 0.0044 MPa, the pressure amplitude of the former changes significantly in the same cavitation cycle, and the cleaning effect is best.

Abstract. Influenza viruses continue to cause epidemics worldwide every year. However, due to the lack of an effective assessment for the severity of influenza epidemics, it was extremely difficult to take preventative measures. Data were extracted from infectious diseases reports from 2011–2018. Joinpoint regression model and susceptible-exposed-infectious-recovered model were built to understand the characteristics and processes of the epidemic. The reported incidence of influenza was 1,913,698 from January 2011 to February 2018, with an average-yearly-reported-incidence-rate of 19.21 per 100,000. However, there had been a substantial nationwide epidemic of influenza after September 2017, when the average yearly reported incidence rate was 87.29 per 100,000 and an annual percentage change of 48.1%. The hemagglutinin genes of most influenza A (H1N1 and H3N2) viruses from the period of the epidemic had lower homology to those before August 2017. All the hemagglutinin of the recommended A (H3N2, H1N1) and B (Victoria) viruses for vaccines 2017/2018 had low matches with the epidemic viruses. The basic reproduction number was 1.53. The vaccination benefit was linearly related to vaccination coverage, while the quarantine measure had only significantly benefited when over 60% of the quarantined population. The most severe epidemic of influenza in China since 2011 occurred during the period from September 2017 to February 2018. Compared to quarantine, influenza vaccination is more effective way to prevent influenza, and strategies to increase vaccination coverage should be taken for the prevention of severe epidemics of influenza.

In practical engineering, the design data are uncertain. The data will deviate from the true value due to technical reasons such as measurement. It would result in the inaccuracy of crack fatigue life prediction. To deal with those problems, a regression model for crack fatigue life prediction is established in this study based on the conditional Bayesian theory. We use the prior distribution instead of posterior distribution in the iteration. The Monte Carlo sampling method is utilized to obtain the likelihood function and the prior distribution of the model. Then, the corresponding posterior distribution of the crack life can be obtained by likelihood and prior in iterative calculation. An engineering example of structural fatigue life of robotic is given to illustrate the application of proposed model. The effects of different parameter uncertainties on the posterior distribution of the model are compared. Also, the results in the least squares method are provided as reference.

In practical engineering, uncertain loads usually cause the variations of structure stiffness to affect the security of the structure. To enhance the reliability and find the optimum structure in engineering, a topology optimization method is developed for the optimization of structural stiffness in this paper. The first-order saddle point approximation method is introduced into the topology optimization process. A multi-constrained stiffness optimization model considering uncertain loads is proposed. The corresponding sensitivity mathematical formula for stiffness is also given. The complete optimization iteration process is given. The structural stiffness optimization problems with the joint constraints of volume and displacement are solved here to illustrate the application of the proposed method. In the examples, a U-shape groove in different working situations is considered which includes the single node displacement constraint and the multi-node displacement constraint. The corresponding optimization results of different working situations are compared, and the results accord with the law of engineering.

An analytical model of laminated composite double-plate system (LCDPS) is established, which efficiently analyzes the common 3D plate structure in engineering applications. The proposed model combines the first-order shear deformation theory (FSDT) and the classical delamination theory, and then the LCDPS’s vibration characteristics are investigated. In the process of analysis, the improved Fourier series method (IFSM) is used to describe the displacement admissible function of the LCDPS, which can remove the potential discontinuities at the boundaries. Five sets of artificial springs are introduced to simulate the elastic boundary constraints, and the restraints of the Winkler elastic layer can be adjustable. The improved Fourier series is substituted into the governing equations and boundary conditions; then, applying the Rayleigh–Ritz method, we take all the series expansion coefficients as the generalized coordinates. After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the free vibration with complex boundary conditions are carried out, including the influence of boundary conditions, lamination scheme, plate geometric parameters, and elastic coefficient between two plates.

Marine flexible pipe/cables, such as umbilicals, flexible pipes and cryogenic hoses, are widely adopted in ocean engineering. The reinforcing armor layer in these pipe/cables is the main component for bearing loads, which is a typical multi-layer helically wound slender structure with different winding angles for different devices. There has been no general theoretical methodology to describe the tensile performance of these flexible pipe/cables. This paper first introduces a theory to solve the tensile mechanical behavior of a helically wound structure. Based on the curved beam theory, a solution of the tensile stress of a helically wound slender is derived. Then, the deformation mechanism of the marine flexible pipe/cables structure with different winding angles is studied. Through comparing theoretical and numerical results, the deformation characteristic of the helically wound slender structure is further explained. It is found that a sectional torsional deformation generates when the structure with a larger winding angle is under tension condition, while the sectional deformation of the structure with a smaller winding angle is mainly tension. Finally, a couple types of marine flexible pipe/cables under the tension condition are provided to analyze the mechanical performance and compare the difference between different theoretical models. The research conclusion from this paper provides a useful reference for the structural analysis and design of marine flexible pipe/cables.

The research object of this paper is the L-shaped plate–cavity coupling system established by a cuboid acoustic cavity with rigid-wall or impedance-wall and L-shaped plate with numerous elastic boundary conditions in view of the Fourier series method. The main research content of this paper is the vibro-acoustic coupling characteristics. In this paper, the displacements admissible functions of the L-shaped plate are generally set as the sum of two cosines’ product and two polynomials. Sound pressure admissible functions of the cuboid acoustic cavity can be considered as the sum of three cosines’ product and six polynomials. The discontinuity of coupling system at all boundaries in the overall solution domain is overcome in this way. Through the energy principle and the Rayleigh-Ritz technology, it can be got that the solving matrix equation of the L-shaped plate-cavity coupling system. Based on verifying the great numerical characteristics of the L-shaped plate–cavity coupling model, they obtained both the frequency analysis and the displacement or sound pressure response analysis under the excitation, including a unit simple harmonic force or a unit monopole source. The advantages of this method are parameterization and versatility. In addition, some new achievements have been shown, based on various materials, boundary conditions, thicknesses, and orthotropic degrees, which may become the foundation for the future research.

Background & aims: Biliary injury is one of the main pathological mechanisms of fulminant hepatic failure (FHF). Delta-like ligand 4 (DLL4)-mediated Notch activation contributes to reversing biliary injury; however, the specific role of DLL4 in biliary restoration is still unclear. This study aimed to determine whether human bone marrow mesenchymal stem cells (hBMSCs) can differentiate into biliary epithelial cells (cholangiocytes) in vitro and in vivo and to clarify the role of DLL4 in restoring damaged liver by enhancing cholangiocyte differentiation. Methods: hBMSCs were transplanted into immunodeficient mice (FRGS) with FHF induced by the hamster-anti-mouse CD95 antibody JO2. The appearance of human cholangiocytes was evaluated in the generated hBMSC-FRGS mice by q-PCR expression, flow cytometry and immunohistochemistry. The potency of DLL4 in inducing cholangiocyte differentiation from hBMSCs was assessed by observing the cell morphology and measuring the expression of cholangiocyte-specific genes and proteins. Results: Human KRT19- and KRT7-double-positive cholangiocyte-like cells appeared in hBMSC-FRGS mice at 12 weeks after transplantation. After these cells were separated and collected by fluorescent-activated cell sorting (FACS), there were high levels of expression of eight typical human cholangiocyte-specific genes and proteins (e.g., KRT19 and KRT7). Furthermore, hBMSC-derived cholangiocytes induced by DLL4 had a better shape with higher nucleus/cytoplasm ratios and showed a specific increase in the expression of cholangiocyte-specific genes and proteins (e.g., KRT19, KRT7, SOX9 and CFTR). Conclusions: Cholangiocytes can be efficiently differentiated from hBMSCs in vivo and in vitro. DLL4 restores damaged liver by enhancing cholangiocyte differentiation from hBMSCs and has the potential to be used in future clinical therapeutic applications.

Direct measurement of the wall pressure loading of the spherical boundary subjected to the near-field underwater explosion is a great difficulty. To investigate the wall pressure caused by electric-spark-generated bubble near a hemispheric boundary, an experiment system is developed. In the method of this experiment, a Hopkinson bar (HPB), used as the sensing element, is inserted through the hole drilled on the hemisphere target and the bar’s measuring end face lies flush with the loaded face of the hemisphere target to detect and record the pressure loading. The semiconductor strain gauges which stick on Hopkinson bar are used to convert the pressure-based signal to the strain wave signal. The bubble in the experiments is formed by a discharge of 400 V high voltage. To validate the pressure measurement technique based on the HPB, an experimental result from pressure transducer is used as the validating system. To verify the capability of this new methodology and experimental system, a series of electric-spark-generated bubble experiments are conducted. From the recorded pressure-time profiles coupled with the underwater explosion evolution images captured by the high-speed camera (HSV), the shock wave pressure loading and bubble collapse pressure loadings are captured in detail at different dimensionless stand-off distances γ from 0.17 to 2.00. From the results of the experiments conducted in this paper, the proposed experiment system can be used to measure the pressure signal successfully, giving new way to study the bubble collapse pressure when the bubble is near a hemispheric boundary. Through the experimental results, the bubbles generated by different dimensionless stand-off distance γ are divided into four categories, and the bubble load characteristics are also discussed.

This paper studies the free vibration characteristics of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory (SFSDT), which contains only four unknown displacement components. The arbitrary straight-sided quadrilateral plate is mapped into a unit square plate uniformly, and accordingly, the problem can be solved directly by the existing vibration modeling method of rectangular plate. The admissible functions of displacements are generally expressed as superposition of the periodic functions based on the improved Fourier series method. All the series expansion coefficients can be determined by the Rayleigh-Ritz procedure. Combined with the artificial virtual spring technology, the present method could be used to analyze the vibration characteristics of quadrilateral plates under arbitrary boundary conditions. Convergence and accuracy of the present method are checked out through some numerical examples of plate with rectangular, skew, trapezoidal and general quadrilateral shapes, and various boundary conditions. In addition, some new results and new conclusions have been given as the benchmark for future research. Keywords: Simple first-order shear deformation theory, Quadrilateral plate, Arbitrary shapes, Improved Fourier series method, Arbitrary boundary conditions, Rayleigh-Ritz technique

This paper establishes a thin orthotropic rectangular fluid–structure coupled system which effectively studies the sound-vibration behaviors. The established coupled system is made up of an acoustic enclosure filled with air or water and a single orthotropic thin plate or parallel double plate on varying elastic Winkler and Pasternak foundations. Based on Fourier series method and classical plate theory (CPT), the admissible functions of the orthotropic plate and cavity could be represented as superposition of the periodic functions. All the unknown series coefficients are gained by the Rayleigh-Ritz method. On the premise of validating the great convergence and accuracy of the established analytical model, both the natural characteristics analysis and the forced response studies under the excitations of a unit monopole source or a unit simple harmonic force are carried out. The effect of various elastic foundations on the fluid–structure coupled system is mainly studied. In addition, some new discoveries have been listed, on the basis of varying orthotropic degrees, boundary constraints and acoustic medium, which could set up the benchmark for the following research. Keywords: Fluid-structure coupled system, Sound-vibration behaviors, Winkler and Pasternak foundations, Fourier series method, Rayleigh-Ritz method

This paper studies the free vibration of arbitrary shaped laminated triangular thin plates based on a modified Fourier series method. An arbitrary shaped triangular plate is mapped into a right-angled isosceles triangular plate with unit length by the coordinate transformation. By padding another right–angled isosceles triangular plate which is near zero thickness on the plate after transformation. The displacement functions are then generally expressed as the combinations of Fourier cosine series and supplementary functions introduced to eliminate the discontinuous or jumping phenomenon in the boundaries. The classical thin plate elasticity theory is employed to construct the energy expressions of the plate. The Rayleigh-Ritz method is used in the present method to obtain all the unknown series expansion coefficients. A number of results are presented to verify the convergence and accuracy of current solution method to laminated triangular thin plates with arbitrary shapes, different material parameters and different boundary conditions. Additionally, some new results are given as the benchmark for future research, which are based on the various boundary conditions and geometric dimensions. Keywords: Free vibration analysis, Thin laminated triangular plate, Arbitrary shapes, Modified Fourier series method, Elastic boundary restraints, Rayleigh-Ritz technique

Abstract Background Interleukin-33 (IL-33) is increasingly being recognized as a key immunomodulatory cytokine in many neurological diseases. Methods In the present study, wild-type (WT) and IL-33−/− mice received intracerebroventricular (i.c.v.) injection of lipopolysaccharide (LPS) to induce neuroinflammation. Intravital microscopy was employed to examine leukocyte–endothelial interactions in the brain vasculature. The degree of neutrophil infiltration was determined by myeloperoxidase (MPO) staining. Real-time PCR and western blotting were used to detect endothelial activation. Enzyme-linked immunosorbent assay and quantitative PCR were conducted to detect pro-inflammatory cytokine levels in the brain. Results In IL-33−/− mice, neutrophil infiltration in the brain cortex and leukocyte–endothelial cell interactions in the cerebral microvessels were significantly decreased as compared to WT mice after LPS injection. In addition, IL-33−/− mice showed reduced activation of microglia and cerebral endothelial cells. In vitro results indicated that IL-33 directly activated cerebral endothelial cells and promoted pro-inflammatory cytokine production in LPS-stimulated microglia. Conclusions Our study indicated that IL-33/ST2 signaling plays an important role in the activation of microglia and cerebral endothelial cells and, therefore, is essential in leukocyte recruitment in brain inflammation. Graphical abstract The role of IL-33/ST2 in LPS induced neuroinflammation

This paper proposes a method for the analysis of acoustic modals and steady-state responses of arbitrary triangular prism and quadrangular prism acoustic cavities based on the three-dimensional improved Fourier series. First, the geometric models of arbitrary triangular prism and quadrangular prism acoustic cavities are established. To facilitate the calculation, the bottom and top surfaces of the irregular cavity are converted into the unit square domain by a coordinate transformation. Internal sound pressure-admissible functions are constructed, and energy expressions are derived after coordinate transformation based on the three-dimensional improved Fourier series. The acoustic modals of arbitrary triangular prism and quadrangular prism acoustic cavities are obtained by the Rayleigh–Ritz technique. At the same time, a point sound source excitation is introduced into the cavity to further study the steady-state responses of prismatic acoustic cavities with different acoustic impedance boundary conditions. The reliability and universality of the method are verified by comparing with the finite element results. The method and results can provide some references and benchmarks for future research and application.

In this study, a compressible three-phase homogeneous model was established using ABAQUS/Explicit. These models can numerically simulate the pulsation process of cavitation bubbles in the free field, near the flat plate target, and near the curved boundary target. At the same time, these models can numerically simulate the strong nonlinear interaction between the cavitation bubble and its nearby wall boundaries. The mutual flow of liquid and gas and fluid solid coupling were solved by the Euler domain in simulation. The results of the numerical simulation were verified by comparing them with the experimental results. In this study, we used electric spark bubbles to represent cavitation bubbles. A high-speed camera was used to record the pulsation process of cavitation bubbles. This study first verified the pulsation process of cavitation bubbles in the free field, because it was the simplest case. Then we verified the interaction process between cavitation bubbles and different wall boundaries. In order to further confirm the credibility of the numerical simulation results, for each wall surface, this study used two burst distances (10 mm and 25 mm) for simulation verification. The numerical model established in this study could effectively simulate the pulsation characteristics of cavitation bubbles, such as the formation of jets and annular bubbles. After verification, the simulated cavitation bubble was almost the same as the cavitation bubble captured by the high-speed camera in the experiment in terms of time, volume, and shape. In this study, a detailed velocity field of the cavitation bubble collapse stage was obtained, which laid down the foundation for the study of the strong nonlinear interaction between the cavitation bubble and the target plates of different shapes. Compared with the experimental results, we found that the numerical model established by the simulation could accurately simulate the bubble pulsation and jet formation processes. In the experiment, the interval time for the bubble pictures taken by the high-speed camera was 41.66 μs per frame. Using a numerical model, the bubble pulsation process can be simulated at an interval of 1 µs per frame. Therefore, the numerical model established by the simulation could show the movement characteristics of the cavitation bubble pulsation process in more detail.

Fiber-reinforced polymer (FRP) composite bridges are usually constructed for rapid installation. The durability of the bridge is increased by stiffness, strength to weight ratio, and corrosion resistance. The main factors on which the design of the composite sandwiched bridge considerably depends are ply layers, material system, alignment of ply angles, and thickness of the core. In this work, a parametric design study for a bridge using finite element analysis (FEA) is presented. Two types of composite materials—carbon fiber reinforced polymer (CFRP) and glass fiber reinforced polymer (GFRP)—were used as the sandwich structure’s skin, and three different types of woods were used as a core. Different design configurations were acquired based on material and instability constraints by using Euro-codes. Failure criterion of Tsai-Hill, Tsai-Wu, MS, equivalent stress, and maximum shear stress were implemented to analyze the overall failure of the bridge deck under Ultimate Limit State (ULS) conditions. The total deformation was examined under Serviceability Limit State (SLS) conditions, and the results were compared and verified by the previous study. The core was also examined using the core-factor and increasing the thickness of the core through parametric modeling.

In order to study the influence of the pressure load generated during the pulsation of cavitation bubbles on the oblique 45-degree curved surface boundary. The curved surface boundaries have different curvatures. This study also designs a multi-angle bracket to make the oblique boundary oblique 45 degrees. This research uses high-voltage electric discharge to generate electric spark bubbles, which act as cavitation bubbles. When the explosion source is at different distances from the oblique 45-degree boundary, a high-speed camera is used to capture the pulsation process of electric spark bubbles. A pressure sensor is used to measure the pulsating load of the electric spark bubbles on the oblique 45-degree boundary during the pulsation process. In this study, we use the dimensionless parameter ζ to represent the curvature of the oblique 45-degree boundary. The dimensionless parameter γ is used to represent the shortest distance between the explosion source and the oblique 45-degree boundary. It is found through experiments that the oscillation characteristics and pulsating load of electric spark bubbles will be affected by ζ and γ. This study summarized six types of unique bubble pulse shapes from 44 groups of experiments. They are “mushroom shape without jet”, “mound shape with jet”, “jellyfish shape with jet”, “oval shape with jet”, “drop shape without jet”, and “spherical shape without jet”. In this paper, the ABAQUS/Explicit is used to simulate the ring-shaped bubble that is not clearly captured by the high-speed camera. Finally, the study summarizes the shock wave load generated during the explosion, the first pulsation load, and the second pulsation load of electric spark bubbles, and finds an obvious overall trend of change.

This investigation proposes a series solution method for free and forced vibration analysis of T-shaped plate structure with general elastic supports, arbitrary coupling angles and elastically coupled conditions. The present solution framework can be readily utilized for various boundary or coupling conditions without modifying the solution algorithms or procedures. The general boundary and coupling conditions are considered with artificial spring method and can be easily achieved with assigning the restraining springs with specified values. In the current approach, the displacement functions for in-plane and bending vibration are expressed as a new form of trigonometric series expansion. The sine terms are introduced to eliminate the discontinuity along the boundary edge or coupling edge. Rayleigh–Ritz method is employed to determine the series expansion coefficients, which are treated as the generalized coordinates. Numerous numerical examples are carried out to verify the accuracy and reliability of the present method. The present method can be directly extended to more complicated structures with any number of plates.

The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and Rayleigh-Ritz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

This paper presents free and forced vibration analysis of airtight cylindrical vessels consisting of elliptical, paraboloidal, and cylindrical shells by using Jacobi-Ritz Method. In this research, the theoretical model for vibration analysis is formulated by Flügge’s thin shell theory and the solution is obtained by Rayleigh-Ritz method. The vessel structure is divided into shell components (i.e., ellipsoid, parabolic, and cylinder) and their segments, and each displacement field of shell segments is represented by the Jacobi polynomials and the standard Fourier series. The continuous conditions at the interface are modeled by using the spring stiffness technique. The reliability and the accuracy of the present method are verified by comparing the results of the proposed method with the results of the previous literature and the finite element method (FEM). Moreover, some numerical results for free and forced vibration of elliptical-cylindrical-elliptical vessel (ECE vessel) and paraboloidal-cylindrical-elliptical vessel (PCE vessel) are reported.

An improved Fourier series method (IFSM) is applied to study the free and forced vibration characteristics of the moderately thick laminated composite rectangular plates on the elastic Winkler or Pasternak foundations which have elastic uniform supports and multipoints supports. The formulation is based on the first-order shear deformation theory (FSDT) and combined with artificial virtual spring technology and the plate-foundation interaction by establishing the two-parameter foundation model. Under the framework of this paper, the displacement and rotation functions are expressed as a double Fourier cosine series and two supplementary functions which have no relations to boundary conditions. The Rayleigh-Ritz technique is applied to solve all the series expansion coefficients. The accuracy of the results obtained by the present method is validated by being compared with the results of literatures and Finite Element Method (FEM). In this paper, some results are obtained by analyzing the varying parameters, such as different boundary conditions, the number of layers and points, the spring stiffness parameters, and foundation parameters, which can provide a benchmark for the future research.

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.

In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.

A generalized Fourier series solution based on the first-order shear deformation theory is presented for the free vibrations of moderately thick rectangular plates with variable thickness and arbitrary boundary conditions, a class of problem which is of practical interest and fundamental importance but rarely attempted in the literatures. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures. Under the current framework, the one displacement and two rotation functions are generally sought, regardless of boundary conditions, as an improved trigonometric series in which several supplementary functions are introduced to remove the potential discontinuities with the displacement components and its derivatives at the edges and to accelerate the convergence of series representations. All the series expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. The effectiveness and reliability of the presented solution are demonstrated by comparing the present results with those results published in the literatures and finite element method (FEM) data, and numerous new results for moderately thick rectangular plates with nonuniform thickness and elastic restraints are presented, which may serve as benchmark solution for future researches.