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Summary: This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the improvement of additive manufacturing as they offer, among many others, excellent stiffness‐to‐weight ratios. We develop here a dedicated HPC solver that benefits from the specific nature of the underlying problem in order to drastically reduce the computational costs (memory and time) for the full fine‐scale analysis of lattice structures. Our purpose is to take advantage of the natural domain decomposition into cells and, even more importantly, of the geometrical and mechanical similarities among cells. Our solver consists in a so‐called inexact FETI‐DP method where the local, cell‐wise operators and solutions are approximated with reduced order modeling techniques. Instead of considering independently every cell, we end up with only few principal local problems to solve and make use of the corresponding principal cell‐wise operators to approximate all the others. It results in a scalable algorithm that saves numerous local factorizations. Our solver is applied for the isogeometric analysis of lattices built by spline composition, which offers the opportunity to compute the reduced basis with macro‐scale data, thereby making our method also multiscale and matrix‐free. The solver is tested against various 2D and 3D analyses. It shows major gains compared to black‐box solvers; in particular, problems of several millions of degrees of freedom can be solved with a simple computer within few minutes. [ABSTRACT FROM AUTHOR]

This paper presents an advanced numerical model based on Carrera unified formulation (CUF) and isogeometric analysis (IGA), the size-dependent finite element unified formulation model is proposed to investigate the static bending and free vibration of laminated composite nano-plate. The CUF type of trigonometric function with nine degrees of freedom is used to simulate the displacement fields of laminated nano-plate. The size effect of nano-plate structures is included through the Eringen’s nonlocal elastic theory. The size-dependent governing equations for static bending and free vibration of laminated are established based on CUF, IGA and nonlocal theory. The correctness of the presented numerical model is verified by comparison with existing solutions. Furthermore, with the addition of a nonlocal effect, the plate’s stiffness decreases correlating to an increase in nonlocal parameter. Through different calculations, the changes in the static and free vibration responses of laminated composite nano-plate are effected by nonlocal parameter, plate length-to-thickness ratio, and boundary conditions including Young’s modulus ratio. [ABSTRACT FROM AUTHOR]

In this paper, an isogeometric dual reciprocity boundary element method (IG-DRBEM) is proposed for the time-domain acoustic wave problem in 3D infinite domain. The fundamental solution of the potential problem is used to establish the boundary-domain integral equation, which avoids the problem of solving the coefficient matrix repeatedly at different times. On the one hand, in order to maintain the dimensionality reduction advantages of the boundary element method, the classical dual reciprocity method is used to transform the domain integral into a boundary integral. On the other hand, for purpose of satisfying the boundary conditions at infinite distance accurately, a reliable integral convergence criterion is established by adopting the approximate variation coefficient. Furthermore, the effects of different approximation functions, variation coefficients, time steps, number of interior points and elements on the results are discussed in detail by several typical examples. Numerical results show that the proposed method has high accuracy and good stability even when analyzing geometrically complex dolphin models. • IGABEM for solving acoustic wave in time domain is proposed for the first time. • The coefficient matrix formed by the boundary integral equation only requires to be calculated once. • The adaptive expansion basis function satisfying the integral regularization condition is proposed. • The multi-patch dolphin model is solved and a stable solution is obtained. [ABSTRACT FROM AUTHOR]

This paper presents a study of large linear systems resulting from the regular B -splines finite element discretization of the c u r l − c u r l and g r a d − d i v elliptic problems on unit square/cube domains. We consider systems subject to both homogeneous essential and natural boundary conditions. Our objective is to develop a preconditioning strategy that is optimal and robust, based on the Auxiliary Space Preconditioning method proposed by Hiptmair et al. [48]. Our approach is demonstrated to be robust with respect to mesh size, and we also show how it can be combined with the Generalized Locally Toeplitz (GLT) sequences analysis presented in [59] in order to derive an algorithm that is optimal and stable with respect to spline degree. Numerical tests are conducted to illustrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

• An efficient numerical framework for magneto-electro-elastic functionally graded porous nanoplate. • The generalized weak form formulation for nonlinear bending of magneto-electro-elastic functionally graded porous nanoplate. • The magneto-electro-elastic model based on Maxwell's equations is established. • The proposed model can high-efficiently predict mechanical, magnetic and electrical coupling. • Some novel benchmark numerical results are illustrated and introduced. We propose an effective approach for geometrically nonlinear analysis of magneto-electro-elastic functionally graded (MEE-FG) porous nanoplate. The key idea relies on a size-dependent isogeometric approach, which is considered as a reliable and interesting technique in this area. A generalized model for MEE-FG nanoplates with porosities satisfies assumptions of the nonlocal Eringen's theory based on von Kármán strains, isogeometric approach and the higher-order shear deformation theory, inherently addressing third derivatives in the approximations. By employing the nonlocal theory, the proposed model effectively illustrates the reduction in nanoplate stiffness under the influence of the nonlocal parameter. We also explore porous distributions across the plate thickness, employing both even and uneven functions, and note that an increase in the porous parameter leads to a more pronounced nonlinear deflection. The electric and magnetic potentials in accordance with Maxwell's equation are denoted. The generalized weak formulation of MEE-FG porous nanoplates is derived by the principle of extended virtual displacement. The influence of small-scale parameter, power law exponent, porosity coefficient and porous distributions on the nonlinear deflection of MEE-FG porous nanoplates is investigated. These findings have significant implications for future research in this field. [ABSTRACT FROM AUTHOR]

We exploit level-set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level-set function, geometry, and solution field are parameterized using the Non-Uniform Rational B-Spline (NURBS) basis functions to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level-set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming. Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies. [ABSTRACT FROM AUTHOR]

The conditioning and spectral properties of the mass and stiffness matrices for acoustic wave problems are here investigated when isogeometric analysis (IGA) collocation methods in space and Newmark methods in time are employed. Theoretical estimates and extensive numerical results are reported for the eigenvalues and condition numbers of the acoustic mass and stiffness matrices in the reference square domain with Dirichlet, Neumann, and absorbing boundary conditions. This study focuses in particular on the spectral dependence on the polynomial degree p, mesh size h, regularity k, of the IGA discretization and on the time step size Δ t and parameter β of the Newmark method. Results on the sparsity of the matrices and the eigenvalue distribution with respect to the number of degrees of freedom d.o.f. and the number of nonzero entries nz are also reported. The results show that the spectral properties of the IGA collocation matrices are comparable with the available spectral estimates for IGA Galerkin matrices associated with the Poisson problem with Dirichlet boundary conditions, and in some cases, the IGA collocation results are better than the corresponding IGA Galerkin estimates, in particular for increasing p and maximal regularity k = p - 1 . [ABSTRACT FROM AUTHOR]

In this paper, the effects of both geometric parameters and mineral density on the evolution of stresses generated in a cementless hip implant are investigated to enable orthopedic surgeons to make an appropriate selection. A design of experiment was used, followed by the analysis of variance (ANOVA) to identify the effects of geometric and physical parameters in terms of bone density on a femoral implant. Twenty-seven implants of different geometric dimensions were considered, without modification of the topology. Multiple regression analysis was chosen to replace the finite element method to predict the level of stresses generated in the stem, in terms of life expectancy, allowing for optimal geometric parameter selection. Three parameters of the stem were selected, namely, stem length (SL), neck length (NL), and neck shaft angle (NSA), where each parameter is apprehended by three levels. Based on a design (3 3) , 27 femur–implant CAD models were created, to analyze the effect of three limiting densities (low, medium, and high) for the estimation of maximum stresses by finite elements. The results obtained by ANOVA for the three densities, respectively, for the low density the SL had an impact of the order of 58.5% on the level of von Mises constraints followed by the NL and NSA. For the medium density, it was observed that the SL remains the most influential parameter, with a rate of 41.2%, while for the high density the NL becomes the most influential (37.5%) followed by the SL and the NSA. The regression model used showed very good accuracy in terms of predicting the level of von Mises stress, compared to the results obtained by the finite element method. [ABSTRACT FROM AUTHOR]

Energy-dependent self-adaptive mesh refinement algorithms are developed for a symmetric interior-penalty scheme for a discontinuous Galerkin spatial discretization of the multi-group neutron diffusion equation using NURBS-based isogeometric analysis (IGA). The spatially self-adaptive algorithms employ both mesh (h) and polynomial degree (p) refinement. The discretized system becomes increasingly ill-conditioned for increasingly large penalty parameters; and there is no gain in accuracy for over penalization. Therefore, optimized penalty parameters are rigorously calculated, for general element types, from a coercivity analysis of the bilinear form. Local mesh refinement allows for a better allocation of computational resources; and thus, more accuracy per degree of freedom. Two a posteriori interpolation-based error measures are proposed. The first heuristically minimizes local contributions to the discretization error, which becomes competitive for global quantities of interest (QoIs). However, for localized QoIs, over energy-dependent meshes, certain multi-group components may become under-resolved. The second employs duality arguments to minimize important error contributions, which consistently and reliably reduces the error in the QoI. [ABSTRACT FROM AUTHOR]

Scale effects play critical roles in the mechanical responses of microstructures. An isogeometric analysis was developed here to investigate the mechanical responses of an axially functionally graded microbeam. The Euler–Bernoulli beam model was utilized, and size effects in the structure were modeled with a stress-driven two-phase local/nonlocal integral constitution. The governing equation of microstructures was given in an equivalent differential form with two additional constitutive boundary conditions. The framework was verified and utilized to analyze the microbeam's static and dynamic mechanical responses. The present work showed great potential for modeling various types of functionally graded microstructures. [ABSTRACT FROM AUTHOR]

Gears are pivotal in mechanical drives, and gear contact analysis is a typically difficult problem to solve. Emerging isogeometric analysis (IGA) methods have developed new ideas to solve this problem. In this paper, a threedimensional body parametric gear model of IGA is established, and a theoretical formula is derived to realize single-tooth contact analysis. Resultswere benchmarked against those obtained fromcommercial software utilizing the finite element analysis (FEA) method to validate the accuracy of our approach. Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test. When juxtaposed with the FEA approach, the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units, all while maintaining comparable accuracy. Notably, the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density, and also significantlymitigated non-physical oscillations in contact stress across the tooth width. This underscores the prowess of IGA in contact analysis. In conclusion, IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling, simulation, and optimization of various mechanical components. [ABSTRACT FROM AUTHOR]

Some of the key features of the isogeometric analysis, IGA, are the capacity of exactly representing the problem geometry, the use of the same basis functions to describe the geometry and the solution field, and a straightforward and automatic discretization refining scheme. The higher order continuity of the isogeometric approximation, important to correctly represent the domain geometry, can be a problem to approximate the displacement field in the neighbourhood of a crack. The eXtended Isogeometric Analysis (XIGA) overcomes this obstacle, enlarging the approximate space of IGA. This is achieved by incorporating customized functions, using the enrichment strategy of the Generalized/eXtended Finite Element Method. When these functions are unknown, they can be computed from the solution of local boundary value problems embracing the crack, and a global–local iterative procedure is established. Here this procedure is firstly proposed to combine FEM and isogeometric approximations, denoted XIGA gl . The effectiveness of this approach is investigated in terms of convergence rates and numerical stability. The method is applied to two-dimensional fracture mechanics problems. The numerical experiments show the importance of using the isogeometric approximation to recover more accurate solutions and minimize the deterioration of the conditioning of the related stiffness matrix. [ABSTRACT FROM AUTHOR]

In computation of flow problems with moving solid surfaces, moving-mesh methods such as the space–time (ST) variational multiscale method enable mesh-resolution control near the solid surfaces and thus high-resolution boundary-layer representation. There was, however, a perception that in computations where the solid surfaces come into contact, high-resolution boundary-layer representation and actual-contact representation without leaving a mesh protection opening between the solid surfaces were mutually exclusive objectives in a practical sense. The introduction of the ST topology change (ST-TC) method in 2013 changed the perception. The two objectives were no longer mutually exclusive. The ST-TC makes moving-mesh computation possible even without leaving a mesh protection opening. The contact is represented as an actual contact and the boundary layer is represented with high resolution. Elements collapse or are reborn as needed, and that is attainable in the ST framework while retaining the computational efficiency at a practical level. The ST-TC now has a 10-year history of achieving the two objectives that were long seen as mutually exclusive. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting flow analysis with boundary layer and contact representation, in the presence of additional intricacies such as geometric complexity, isogeometric discretization, and rotation or deformation of the solid surfaces. The flow analyses conducted with these ST methods include car and tire aerodynamics with road contact and tire deformation and ventricle-valve-aorta flow. To help widen awareness of these methods and what they can do, we provide an overview of the methods, including those formulated in the context of isogeometric analysis, and the computations performed over the 10-year history of the ST-TC. [ABSTRACT FROM AUTHOR]

The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical features many elements may be required, possibly leading to unnecessarily large computation costs. Without loss of accuracy, a reduction in computation cost can be achieved by integrating geometry representation and solution approximation into a single framework using the isogeometric analysis (IGA) paradigm. In this study, we propose an IGA framework suitable for echocardiogram data of cardiac mechanics, where we show the advantageous properties of smooth splines through the development of a multi-patch anatomical model. A nonlinear cardiac model is discretized following the IGA paradigm, meaning that the spline geometry parametrization is directly used for the discretization of the physical fields. The IGA model is benchmarked with a state-of-the-art biomechanics model based on traditional FEM. For this benchmark, the hemodynamic response predicted by the high-fidelity FEM model is accurately captured by an IGA model with only 320 elements and 4700 degrees of freedom. The study is concluded by a brief anatomy-variation analysis, which illustrates the geometric flexibility of the framework. The IGA framework can be used as a first step toward an efficient workflow for an improved understanding of, and clinical decision support for, the treatment of cardiac diseases like heart rhythm disorders. [ABSTRACT FROM AUTHOR]

• Small scale analysis of functionally graded triply periodic minimal surface (FG-TPMS) nanoplates. • The generalized weak form formulation for the FG-TPMS nanoplate is proposed. • A fitting technique based on a two-phase piece-wise function for porous structures of TPMS. • The length scale parameters can high-efficiently predict size effects. • Novel benchmark numerical results are illustrated and introduced. In recent years, the triply periodic minimal surface (TPMS) has emerged as a remarkable solution for constructing structures, drawing inspiration from natural architectures. TPMS offers several outstanding features, including porous architectures with high interconnectivity, smooth surfaces and the ability to achieve mathematically controllable geometry features. However, it is evident that the current research has not fully harnessed the extensive potential and benefits of TPMS structures. In this paper, a groundbreaking approach for analyzing functionally graded triply periodic minimal surface (FG-TPMS) nanoplate, which is utilized a novel nonlocal strain gradient isogeometric analysis, is provided. Three patterns of the FG-TPMS nanoplate, namely Primitive (P), Gyroid (G) and I-gragh and Wrapped Package-graph (IWP), are utilized in this study. The primary focus is to investigate size dependent problems with two types of density distributions. The proposed model successfully incorporates both nonlocal effects and strain gradient effects into nanoplate structures. The paper demonstrates how the mechanisms responsible for both reducing and enhancing stiffness in the nanoplate can be understood by fine-tuning the nonlocal and strain gradient parameters. The findings of this study offer promising prospects for future design and optimization as they provide a robust approach to address the complex mechanical behavior observed in the FG-TPMS nanoplate. The proposed model not only captures the behavior accurately but also opens up new avenues for exploring the capabilities of FG-TPMS structures. [ABSTRACT FROM AUTHOR]

In this paper, we consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e. vector-valued mapped piecewise polynomials lying in the H (div) space which appropriately approximate the desired divergence constraint. Our estimates are constant-free in the leading term, locally efficient, and robust with respect to the polynomial degree. They are also robust with respect to the number of hanging nodes arising in adaptive mesh refinement employing hierarchical B-splines, though not with respect to the smoothness and support overlaps. Two partitions of unity are designed, one with larger supports corresponding to the mapped splines, and one with small supports corresponding to mapped piecewise multilinear finite element hat basis functions. The equilibration is only performed on the small supports, avoiding the higher computational price of equilibration on the large supports or even the solution of a global system. Thus, the derived estimates are also as inexpensive as possible. An abstract framework for such a setting is developed, whose application to a specific situation only requests a verification of a few clearly identified assumptions. Numerical experiments illustrate the theoretical developments. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, isogeometric analysis (IGA) and nonlocal theory are used to investigate the free vibration and transient response of bidirectional functionally graded porous (BFGP) curved nanobeams with elastic boundary conditions (BCs) and variable nonlocal parameters. Different from traditional boundary conditions, where a curved beam's beginning and end positions are connected by an elastic system of straight and torsion springs, this allows for greater flexibility in controlling the stiffness of the springs to obtain arbitrary boundaries. One thing that sets this research apart from others is the hypothesis that the mechanical characteristics of the materials, including nonlocal parameters, are supposed to change according to Voigt schemes in the direction of thickness, length, and porosities of the beam. On the basis of higher-order shear curved beam theory, Hamilton's principle is used to develop the curved nanobeam's equations of motion. The accuracy of the proposed model is established by juxtaposing the current study's findings with those of credible papers. A comprehensive examination has been conducted to analyze the impact of input parameters on the free vibration and transient response of BFGP curved nanobeams. Furthermore, the benchmark solutions elucidated in this work might serve as a valuable reference for analyzing the free vibration and transient response of BFGP curved nanobeams in other investigations. [ABSTRACT FROM AUTHOR]

In this paper, a new isogeometric topology optimization (ITO) method based on the moving iso-surface threshold (MIST) method is proposed, and the corresponding MATLAB code is provided. The same nonuniform rational B-splines (NURBS) basis functions are used to construct a geometrical model and evaluate the objective function for minimal compliance problems. In MIST-based ITO, the physical response function is calculated by using the same NURBS basis functions as the geometry model. First, the physical response function values of control points are calculated by using the NURBS basis function and the physical response function values of the Gauss points. Second, the physical response function values of the knots (the element nodes) are obtained by fitting the control points using NURBS basis functions. Finally, the physical response surface is formed by connecting its nodal values. The structure topology is iteratively updated by using an iso-surface with an appropriate threshold to cut the physical response surface. Compared to traditional MIST, MIST-based ITO can improve the computational accuracy and computational efficiency of high-order elements. Several numerical examples demonstrate the effectiveness of the proposed method, verifying the validity of isogeometric topology optimization MATLAB codes in implementing MIST_based_ITO, which is provided in Online Appendix 1. [ABSTRACT FROM AUTHOR]

Energy-dependent self-adaptive mesh refinement algorithms are developed for a continuous Bubnov-Galerkin spatial discretization of the multi-group neutron diffusion equation using NURBS-based isogeometric analysis (IGA). The spatially self-adaptive algorithms employ both mesh (h) and polynomial degree (p) refinement. Constraint-based equations are established across irregular interfaces with hanging-nodes; they are based upon master-slave relationships and the conservative interpolation between surface meshes. A similar Galerkin projection is employed in the conservative interpolation between volume meshes to evaluate group-to-group source terms over energy-dependent meshes; and to evaluate interpolation-based error measures. Enforcing continuity over an irregular mesh does introduce discretization errors. However, local mesh refinement allows for a better allocation of computational resources; and thus, more accuracy per degree of freedom. Two a posteriori interpolation-based error measures are proposed. The first heuristically minimizes local contributions to the discretization error, which becomes competitive for global quantities of interest (QoIs). However, for localized QoIs, over energy-dependent meshes, certain multi-group components may become under-resolved. The second employs duality arguments to minimize important error contributions, which consistently and reliably reduces the error in the QoI. [ABSTRACT FROM AUTHOR]

One of the prevalent challenges in the design, numerical analysis, and verification of structural membranes lies in the non-linearity of their loadresponse curves. Structural analysis has to be performed with a geometrically non-linear approach due to the interaction of form and forces, and thus a linear extrapolation or combination of analysis results is not possible. The appropriate modeling of the environmental impacts (such as wind and snow) also has a significant influence on the analysis results. Furthermore, non-linear material behavior can be of interest. The resulting load-response curves (e.g. stresses and deformations) are typically non-linear and their interpretation towards the underlying safety requirements is not straight forward. In addition, the prestress also has a major influence on membranes' structural behavior. However, the current European regulations for the proof of the limit states (ULS and SLS) of any building require a simplified categorization of the structural behavior. This research investigates the load-bearing behavior of typical re occurring membrane shapes in the context of current verification requirements. Typical load cases are applied and the structural behavior is shown under consideration of the mentioned non-linearities. [ABSTRACT FROM AUTHOR]

Isogeometric analysis (IGA) is known to show advanced features compared to traditional finite element approaches. Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functional grading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward a deep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complex IGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trained using the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationship between the outputs and the inputs is constructed using machine learning so that the displacements can be directly estimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA and obtain the displacement responses for different loads and gradient indexes. Results show that the recognition error is low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA for modeling the geometrically nonlinear bending behavior of FG plates. [ABSTRACT FROM AUTHOR]

In this work, a novel refined higher-order shear deformation plate theory is integrated with nonlocal elasticity theory for analyzing the free vibration, bending, and transient behaviors of fluid-infiltrated porous metal foam piezoelectric nanoplates resting on Pasternak elastic foundation with flexoelectric effects. Isogeometric analysis (IGA) and the Navier solution are applied to the problem. The innovation in the present study is that the influence of the inplane variation of the nonlocal parameter on the free and forced vibration of the piezoelectric nanoplates is investigated for the first time. The nonlocal parameter and material characteristics are assumed to be material-dependent and vary gradually over the thickness of structures. Based on Hamilton's principle, equations of motion are built, then the IGA approach combined with the Navier solution is used to analyze the static and dynamic response of the nanoplate. Lastly, we investigate the effects of the porosity coefficients, flexoelectric parameters, elastic stiffness, thickness, and variation of the nonlocal parameters on the mechanical behaviors of the rectangular and elliptical piezoelectric nanoplates. [ABSTRACT FROM AUTHOR]

Porous structures by additive manufacturing have fascinating and compelling performance compared with solid structures. The stress‐related porous infill designs which could greatly mitigate the effects of the intrinsic high residual stress in additive manufacturing process have gained increasing attention. In the current work, we propose a promising Isogeometric Topology Optimization (ITO) method for porous infill structures with stress minimization to avoid the occurrence of stress concentrations in additive manufacturing. The IsoGeometric Analysis (IGA) and induced p‐norm aggregation are utilized to develop a stress‐minimization topology description model for infill design, which can remove the mesh dependency and offer benefits for improving numerical accuracy and convergence stability. We also introduced global volume constraints to easily control the usage of material and eliminate the over‐fine structures affecting the printing accuracy. Several numerical examples are performed to demonstrate the effectiveness and advantages of the proposed ITO method on porous infill designs with stress minimization. The laser powder bed fusion (LPBF) technique is employed to fabricate several prototypes, and the performance are evaluated by experiments. The advancements of our work are demonstrated effectively, which is adapted for additive manufacturing and practical application. [ABSTRACT FROM AUTHOR]

Point cloud registration has various applications within the computer-aided design (CAD) community, such as model reconstruction, retrieving, and analysis. Previous approaches mainly deal with the registration with a high overlapping hypothesis, while few existing methods explore the registration between low overlapping point clouds. However, the latter registration task is both challenging and essential, since the weak correspondence in point clouds usually leads to an inappropriate initialization, making the algorithm get stuck in a local minimum. To improve the performance against low overlapping scenarios, in this work, we develop a novel algorithm for accurate and robust registration of low overlapping point clouds using optimal transformation. The core of our method is the effective integration of geometric features with the probabilistic model hidden Markov random field. First, we determine and remove the outliers of the point clouds by modeling a hidden Markov random field based on a high dimensional feature distribution. Then, we derive a necessary and sufficient condition when the symmetric function is minimized and present a new curvature-aware symmetric function to make the point correspondence more discriminative. Finally, we integrate our curvature-aware symmetric function into a geometrically stable sampling framework, which effectively constrains unstable transformations. We verify the accuracy and robustness of our method on a wide variety of datasets, particularly on low overlapping range scanned point clouds. Results demonstrate that our proposed method attains better performance with higher accuracy and robustness compared to representative state-of-the-art approaches. [Display omitted] • New registration method combining geometric features with hidden Markov random field. • Novel objective function incorporating curvature geometry with symmetric function. • A curvature-aware point pair sampling process improving the registration stability. • Extensive experiments and comparisons with representative state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The inflation of hyperelastic thin shells is a highly nonlinear problem that arises in multiple important engineering applications. It is characterised by severe kinematic and constitutive nonlinearities and is subject to various forms of instabilities. To accurately simulate this challenging problem, we present an isogeometric approach to compute the inflation and associated large deformation of hyperelastic thin shells following the Kirchhoff–Love hypothesis. Both the geometry and the deformation field are discretized using Catmull–Clark subdivision bases which provide the required C 1 -continuous finite element approximation. To follow the complex nonlinear response exhibited by hyperelastic thin shells, inflation is simulated incrementally, and each incremental step is solved using the Newton–Raphson method enriched with arc-length control. An eigenvalue analysis of the linear system after each incremental step assesses the possibility of bifurcation to a lower energy mode upon loss of stability. The proposed method is first validated using benchmark problems and then applied to engineering applications, where the ability to simulate large deformation and associated complex instabilities is clearly demonstrated. [ABSTRACT FROM AUTHOR]

The present study employs isogeometric analysis (IGA) to investigate the shear buckling instability of functionally graded porous nanocomposite folded (FG-PNF) plates reinforced by graphene platelets (GPLs). The distribution of GPLs along the thickness direction is assumed to be uniform or non-uniform, and both symmetric and asymmetric porosity distributions are included. The weak form equation is derived using a logarithmic higher-order shear deformation theory (HSDT) as a displacement field according to the principle of virtual work. To analyze folded plates, the geometry is divided into two patches, and the stability equations of each patch are discretized using IGA as a reliable and effective numerical method. The stiffens and geometric stiffness matrices of each patch are transformed into the global coordinate system for assembling, and the continuity condition along the intersection line is satisfied by adding the stiffness matrix of the bending strip to the total stiffness matrix of the FG-PNF plate. A comprehensive comparison study is conducted to demonstrate the accuracy and reliability of the proposed methodology. Finally, parametric studies are carried out to investigate the effects of FG distribution of materials, crank angle, general boundary conditions and geometrical parameters on the critical shear buckling load of FG-LNF plates. [ABSTRACT FROM AUTHOR]

An optimal electric machine design task can be posed as a constrained multi-objective optimization problem. While the objectives require time-consuming finite element analysis, constraints, such as geometric constraints, can often be based on mathematical expressions. This article investigates this mixed computationally expensive optimization problem and proposes a computationally efficient optimization method based on evolutionary algorithms. The proposed method always generates feasible solutions by using a generalizable repair operator and also addresses time-consuming objective functions by incorporating surrogate models for their prediction. The article successfully establishes the superiority of the proposed method over a conventional optimization approach. This study demonstrates how a complex engineering design task can be optimized efficiently for multiple objectives and constraints requiring heterogeneous evaluation times. It also shows how optimal solutions can be analysed to select a single preferred solution and harnessed to reveal vital design features common to optimal solutions as design principles. [ABSTRACT FROM AUTHOR]

In this article, a novel numerical approach based on electromechanical coupling isogeometric analysis employing a piecewise linear zig-zag function is proposed for modeling and analysis of smart constrained layer damping (SCLD) treatment in multilayer porous functionally graded graphene platelets-reinforced composite (PFG-GPRC) plates. The approach efficiently approximates the geometric, mechanical, and electric displacement fields by utilizing non-uniform rational B-splines (NURBS) basis functions. These basis functions are subsequently integrated with the zig-zag formulation to characterize the system dynamic and help handle both continuous/discontinuous material properties at all interfaces, as well as improve the effectiveness of global–local numerical solutions for the analysis of current structures. The multilayer PFG-GPRC plate model is designed to incorporate porous, uniformly, or non-uniformly distributed layers based on three different graphene platelet patterns. The analysis of the SCLD treatment encompasses an examination of the frequency response function of the damped structure under passive/hybrid mechanisms, taking into account viscoelastic behavior and the converse piezoelectric effect. Reliability in the current analysis is demonstrated through a validation study, and a comprehensive parametric investigation is undertaken to analyze the impact of various parameters related to graphene platelets (GPLs) and distribution types of porosity on the damping behavior of multilayer PFG-GPRC plates. [ABSTRACT FROM AUTHOR]

To solve nonlinear dynamic problems in three-dimensional space, this investigation presents a new isogeometric solid element and nonlinear strain field of the proposed element through coordinate transformation in tensor analysis. In order to make the proposed element can be used seamlessly in computer aided design (CAD) and computer aided engineering (CAE) systems, trivariate T-spline is adopted as the basis function of the isogeometric solid element. Local mesh update algorithms are developed for T-spline based isogeometric solid element in virtue of Bézier projection method. Mesh is refined locally in important regions to obtain accurate results and redundant elements are coarsened beyond important regions to improve computational efficiency. Therefore, the computational efficiency and the computational accuracy are balanced in nonlinear dynamics analysis. Three statics numerical examples are set to test the correctness of the elemental elastic model. A flexible pendulum simulation is performed to study the dynamics characteristic of the proposed element. An experiment is implemented to test the proposed element’s ability to solve nonlinear dynamics problems. A simulation that a flexible pendulum contacts with a stick is performed and local mesh update algorithms are employed. The computation results and computation time are analyzed to research the effectiveness of the proposed locally varying mesh T-spline based solid element in nonlinear dynamics problems. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive investigation of novel frameworks for graphene platelets reinforced functionally graded triply periodic minimal surface (GPLR-FG-TPMS) plates. Three functional grading frameworks, which focus on controlling mass density, elastic modulus, and shear modulus, are proposed, each incorporating three porosity distributions in combination with three GPL volume fraction distributions. Three sheet-based TPMS structures including Primitive, Gyroid, and I-graph and Wrapped Package-graph are explored in this study. The static and free vibration analyses of these plates are conducted using a five-variable plate theory model with isogeometric analysis (IGA). The key parameters in each framework, including porosity coefficients and GPL weight fractions, are attentively studied. Their influences on plate responses are indicated corresponding to each porosity and GPL volume distribution. Notably, the mass density framework exhibits significant potential as a means of comparing different porous cores. It can further provide an approximate stiffness-to-weight ratio with a great lower weight compared to others. In this framework, the fundamental frequency of the plate can be achieved at approximately 95% of the frequency obtained with 0.97 and 0.98 weight in the elastic modulus and shear modulus frameworks, respectively, while utilizing only 0.35 of the total weight. To demonstrate the efficiency of the novel FG plate models, two cellular solids are also adopted in computations. The comparison of these structures in all three frameworks together with different porosity distributions is presented using polar charts. Remarkably, we find that in the context of thick plates, Primitive plates exhibit superior performance among all the plates. In general, this research tries to shed light on the development of advanced GPLR-FG-TPMS plates, elucidating the effects of different functional grading frameworks and guiding the design of lightweight and mechanically efficient structures. • Three novel functional grading frameworks that control mass density, elastic modulus, and shear modulus are proposed. • GPL-FG-TPMS plates are studied in various porosity and GPL volume fraction distributions. • Superiority and limitations of each functional grading approach are indicated. • P, G, IWP, and two cellular structures are compared guiding lightweight and mechanically efficient structural designs. [ABSTRACT FROM AUTHOR]

One of the major challenges in finite element methods is the mitigation of spurious oscillations near sharp layers and discontinuities known as the Gibbs phenomenon. In this paper, we propose a set of functionals to identify spurious oscillations in best approximation problems in finite element spaces. Subsequently, we adopt these functionals in the formulation of constraints in an effort to eliminate the Gibbs phenomenon. By enforcing these constraints in best approximation problems, we can entirely eliminate over- and undershoot in one-dimensional continuous approximations, and significantly suppress them in one- and higher-dimensional discontinuous approximations. [ABSTRACT FROM AUTHOR]

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication. The expression of the geometric stiffness matrix is derived, the finite element linear buckling analysis is conducted, and the sensitivity solution of the linear buckling factor is achieved. For a specific problem in linear buckling topology optimization, a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells. The aggregation function method is used to consider the high-order eigenvalues, so as to obtain continuous sensitivity information and refined structural design. With cyclic matrix programming, a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted. To maximize the buckling load, under the constraint of the given buckling load, two types of topological optimization columns are constructed. The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm. The vertex method and the matching point method are used to carry out an uncertainty propagation analysis, and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance. Finally, the differences in the structural topology optimization under different reliability degrees are illustrated by examples. [ABSTRACT FROM AUTHOR]

The sound barrier is an important means to reduce noise caused by traveling vehicles on roads or railways. Structural design and optimization of the sound barrier can effectively reduce the use of materials and improve the noise reduction effect. In this paper, a new isogeometric singular boundary method is proposed and applied to the shape optimization of sound barriers. The geometric structure is accurately represented by using non-uniform rational B-splines. The acoustic shape sensitivity of the control points was calculated using the direct differentiation method and the adjoint variable method. After that, the method of moving asymptotes is adopted as an optimizer to search for the optimal layout of the design objective. In the numerical procedure, the shoelace formula is introduced to calculate the area of the closed structure, which only uses the discrete node information on the boundary. The proposed approach completely avoids the mesh division in the finite element method as well as the singular integral calculation in the boundary element method. More importantly, it can be seamlessly connected with the computer-aided design system for the subsequent treatment by engineers. Three numerical examples are provided to illustrate the accuracy and effectiveness of the proposed isogeometric method. This work provides a simple and effective way for the structural optimization design of sound barriers. [ABSTRACT FROM AUTHOR]

A high-precision semi numerical and semi analytical method for interfacial fracture problem of piezo- electric quasicrystals (PQCs)/piezoelectric crystals (PZCs)/elastic material composites with notches was de- veloped. Firstly, the Hamiltonian system was introduced and the Hamiltonian dual equations for the 3-material composite were formulated. The higher order partial differential governing equations were transformed into a set of ordinary differential equations. Secondly, the symplectic eigenvalues and eigensolutions were obtained through separation of variables. The physical quantities were expressed with the expansion of symplectic series. Finally, a symplectic isogeometric analysis (IGA) coupling equation was derived through combination of the symplectic series and the IGA. The analytical expressions of the physical quantities near the notch tip and the intensity factors were derived. [ABSTRACT FROM AUTHOR]