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This paper presents, for the first time, an effective numerical approach based on the isogeometric analysis (IGA) and the six-variable quasi-three dimensional (3D) higher-order shear deformation theory (HSDT) to study the free vibration characteristics of functionally-graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) plates submerged in a fluid medium. The plate theory incorporates the thickness stretching and the effects of transverse shear deformation without using any shear correction factors. The velocity potential function and Bernoulli's equation are used to derive the hydrodynamic pressure acting on the plate surface. Both horizontally and vertically immersed plate configurations are considered here in the form of inertia effects. The plates are composed of multilayer GOEAMs, with the GOri content varying through the plate's thickness in a layer-wise manner. This design results in graded auxetic growth. The material properties are evaluated by mixing rules and a genetic programming (GP)-assisted micromechanical model. The governing equations of motion for the FG-GOEAM plates immersed in a fluid medium are derived by Hamilton's principle. After validating the convergence and accuracy of the present model, a comprehensive parametric study is carried out to examine the effects of the GOri content, GOri distribution pattern, GOri folding degree, fluid level, immersed depth, and geometric parameter on the natural frequencies of the FG-GOEAM plates. The results show that the natural frequencies for the four GOri distribution patterns increase with the increase in the layer number when the lay number is fewer than 10, and then stabilize after the layer number reaches 10. Besides, in general, the natural frequency of the FG-GOEAM plate in a vacuum or fluid increases when the GOri content increases, while decreases when the GOri folding degree increases. Some additional findings related to the numerical results are presented in the conclusions. It is believed that the present results are useful for the precise design and optimization of FG-GOEAM plates immersed in a fluid medium. [ABSTRACT FROM AUTHOR]

Isogeometric analysis (IGA) has been widely used as a spatial discretization method for phase field models since the seminal work of Gómez et al. (Comput. Methods Appl. Mech. Engrg. 197(49), pp. 4333–4352, 2008), and the first numerical convergence study of IGA for the Cahn-Hilliard equation was presented by Kästner et al. (J. Comput. Phys. 305(15), pp. 360–371, 2016). However, to the best of our knowledge, the theoretical convergence analysis of IGA for the Cahn-Hilliard equation is still missing in the literature. In this paper, we provide the convergence analysis of IGA for the multi-dimensional Cahn-Hilliard equation for the first time. The two important steps to carry out the convergence analysis are (1) we rigorously prove that the L ∞ norm of IGA solution is uniformly bounded for all mesh sizes, and (2) we construct an appropriate Ritz projection operator for the bi-Laplacian term in the Cahn-Hilliard equation. The first- and second-order stabilized semi-implicit schemes are used to obtain the fully discrete schemes. The energy stability analyses are rigorously proved for the resulting fully discrete schemes. Finally, several two- and three-dimensional numerical examples are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

• Isogeometric modeling of the flow-excited cavity-plate-exterior space coupled system. • Transferring pressure data from CFD into the isogeometric vibro-acoustic model. • Natural frequencies of the cavity-plate-exterior space coupled system. • Cavities with irregular geometries such as convex or concave shapes. The flow-induced noise has become an important noise source in marine sonar self-noise, which can adversely affect the normal operation of sonar. The marine sonar cabin is simplified as a cavity-plate-exterior space coupled system whose flow-induced vibro-acoustic characteristics are investigated in this paper. An isogeometric vibro-acoustic formulation is proposed in which the cavity with an irregular geometry is precisely described by adjusting the control points and corresponding weights. The flow-induced vibro-acoustic response is obtained by transferring the turbulent pressure data from computational fluid dynamics into the isogeometric vibro-acoustic model. Imposing turbulent pressure into the isogeometric control points is proposed to achieve this objective using a node-based interpolation method. The vibro-acoustic modeling is validated and compared with previous experimental results. These comparisons demonstrate that the developed formulation accurately predicts the vibro-acoustic characteristics of the fluid-excited coupled system. The influences of flow speed, acoustic medium, and cavity shape on flow-excited vibration and sound radiation are discussed. Results show a decrease in radiated acoustic power and radiation efficiency in the exterior space, and a shift in the plate-exterior space coupling modal frequency to lower frequencies when the cavity changes from convex to concave. [ABSTRACT FROM AUTHOR]

This paper introduces a novel isogeometric analysis-reuse framework called IGA-Graph-Net, which combines Graph Neural Networks with Isogeometric Analysis to overcome the limitations of Convolutional Neural Networks when dealing with B-spline data. Our network architecture incorporates ResNetV2 and PointTransformer for enhanced performance. We transformed the dataset creation process from using Convolutional Neural Networks to Graph Neural Networks. Additionally, we proposed a new loss function tailored for Dirichlet boundary conditions and enriched the input features. Several examples are presented to demonstrate the effectiveness of the proposed framework. In terms of accuracy when tested on the same set of partial differential equation data, our framework demonstrates significant improvements compared to the reuse method based on Convolutional Neural Networks for Isogeometric Analysis on topology-consistent geometries with complex boundaries. [ABSTRACT FROM AUTHOR]

• A stress-constrained CMTO for designing porous composites using discrete material optimisation is proposed. • The proposed method is validated by effectively designing the structural configurations and material distributions. • Over 30 % decrease in maximum stress of the cases for porous omposites is achieved using the proposed method. • It is found that an "interface-enlarging" phenomenon is also observed using the stress-constrained CMTO. Porous composites have attracted increasing attention in recent decades. This study develops a concurrent multiscale topology optimisation (CMTO) method under a prescribed stress constraint for designing porous composites with multi-domain microstructures. First, to address the difficulty of predicting local stress due to varying of microstructural type throughout the optimisation process, a continuous and differentiable stress measure is proposed to effectively approximate the local stress. Second, an inverse homogenisation method based on isogeometric analysis (IGA) is developed to improve the accuracy of stress prediction, and then it is integrated into a CMTO which is developed based on the discrete material optimisation (DMO) interpolation scheme. Third, a stress constraint which is differentiable with respect to both macro and micro design variables is proposed to enable the stress-constrained concurrent optimisation of the macrostructural configuration, microstructural configuration and distribution. Fourth, a novel post-processing approach is established to achieve smooth while volume preserving contour of unit cells with layouts. Finally, two benchmark design examples, namely l-bracket and Crack problems, are implemented using the presented CMTO under a global stress constraint to demonstrate the effectiveness of the proposed method. The result indicates that the proposed method can effectively decrease the stress concentration via three design manners, i.e., the macrostructural configuration, microstructural configuration and distribution. Also, an "interface-enlarging" phenomenon was interestingly but reasonably found in those cases when subjected to stress-constraint considerations. [ABSTRACT FROM AUTHOR]

• A novel model is proposed to analyze nonlinear behaviors of intelligent structures. • Experiment on smart sandwich plate is tested to verify the proposed SLHSDT-IGA. • GPLs and piezoelectric materials are attempted to resist large deformation. Piezoelectric materials as the controlling element have been widely utilized to produce intelligent engineering structures, while these smart structures may fail to realize effective control of composite structures with large deformations. However, investigations on such issues are less reported in published literature, as an accurate and efficient model is required to well forecast the geometrically nonlinear behaviors of smart sandwich structures. As a result, a novel sinusoidal Legendre global-local higher-order shear deformation plate theory (SLHSDT) has been developed to accurately capture geometrically nonlinear behaviors of piezoelectric sandwich plates. The proposed model can fulfill the compatible conditions of transverse shear stresses and contain transverse normal strain, which can ensure precision in predicting electromechanical behaviors. The multi-patch isogeometric analysis (IGA) method for sandwich plates partially bonded with piezoelectric layers is proposed to overcome C1-continuity between patches for the first time. Moreover, the Newmark- β method and Newton-Raphson technique are attempted to solve the nonlinear equations. The present model has been utilized to investigate electromechanical behaviors of laminated structures with piezoelectric layers, which has been compared with the published results. In addition, experiments on macro fiber composite (MFC) integrated sandwich plates have been also carried out in the present work, which can effectively verify the performance of proposed model. Subsequently, the proposed model is employed to study electromechanical behaviors of the five-layer piezoelectric sandwich plates containing internal pores and graphene platelets. Then, influences of the porosity coefficient and GPLs weight fraction on the nonlinear electromechanical behaviors of sandwich plates are investigated. Eventually, the active control on nonlinear behaviors of piezoelectric porous sandwich plates with GPLs reinforcement is studied by using a closed-loop control system, and an effective approach slowing down large deformation has been proposed by selecting an appropriate distribution of GPLs along the thickness direction. [ABSTRACT FROM AUTHOR]

Neurodevelopmental disorders (NDDs) have arisen as one of the most prevailing chronic diseases within the US. Often associated with severe adverse impacts on the formation of vital central and peripheral nervous systems during the neurodevelopmental process, NDDs are comprised of a broad spectrum of disorders, such as autism spectrum disorder, attention deficit hyperactivity disorder, and epilepsy, characterized by progressive and pervasive detriments to cognitive, speech, memory, motor, and other neurological functions in patients. However, the heterogeneous nature of NDDs poses a significant roadblock to identifying the exact pathogenesis, impeding accurate diagnosis and the development of targeted treatment planning. A computational NDDs model holds immense potential in enhancing our understanding of the multifaceted factors involved and could assist in identifying the root causes to expedite treatment development. To tackle this challenge, we introduce optimal neurotrophin concentration to the driving force and degradation of neurotrophin to the synaptogenesis process of a 2D phase field neuron growth model using isogeometric analysis to simulate neurite retraction and atrophy. The optimal neurotrophin concentration effectively captures the inverse relationship between neurotrophin levels and neuron survival, while its degradation regulates concentration levels. Leveraging dynamic domain expansion, the model efficiently expands the domain based on outgrowth patterns to minimize degrees of freedom. Based on truncated T-splines, our model simulates the evolving process of complex neurite structures by applying local refinement adaptively to the cell/neurite boundary. Furthermore, a thorough parameter investigation is conducted with detailed comparisons against neuron cell cultures in experiments, enhancing our fundamental understanding of the possible mechanisms underlying NDDs. [ABSTRACT FROM AUTHOR]

A novel Isogeometric topology optimization (ITO) method considering stress constraint and load uncertainties is proposed for the fiber reinforced composite structures. Firstly, with the density and fiber orientations at the control points of Non-Uniform Rational B-Splines (NURBS) defined as design variables while the magnitudes and direction angles of uncertain external loads described as interval variables, the ITO model for the fiber reinforced composite structures is constructed to minimize the structural compliance under the constraints on both material usage and global failure coefficient. To accurately calculate the material properties and stress distribution within fiber reinforced composite structures, the Gauss subdivision and the Tsai-Hill criterion combined with the P-norm function are introduced. Further, the critical loads leading to the worst structural performance are determined based on the weighted Sigmoid penalty of the stress constraint for balancing the performance requirements of high stiffness and high strength. Finally, the ITO model is solved by integrating all the proposed innovations with the Method of Moving Asymptotes (MMA). The validity and effectiveness of the proposed ITO method are validated by both numerical and engineering examples. [ABSTRACT FROM AUTHOR]

• A novel trimmed-NURBS-based isogeometric analysis method. • Thermal buckling analysis of composite panels with curvilinear fibers. • A segmented density scheme to avoid localized eigenmodes. • An artificial shearing factor to avoid shearing locking phenomenon. The isogeometric analysis of variable-stiffness structures with curvilinear fibers has gained considerable research attention. However, dealing with structures that have complex cutouts poses challenges for isogeometric analysis. Additionally, the thermal-elastic behavior of variable-stiffness structures must be carefully considered, as they often operate in thermal environments. This study introduces a novel trimmed non-uniform rational basis spline (NURBS) method to address these challenges and investigate the thermal buckling behavior of variable-stiffness plates. The method generates trimmed NURBS elements using a level-set function on the initial NURBS mesh to describe complex geometries. Segmented density interpolation formulas are proposed to capture the contributions of different NURBS elements and to prevent localized eigenmodes. An artificial shear correction factor is introduced to mitigate shear locking. Several numerical examples with various boundary conditions and fiber configurations, are presented to demonstrate the high accuracy and low computational costs of the proposed method. [ABSTRACT FROM AUTHOR]

Piezoelectric heterogeneous materials are widely used in flexible electronic device design, enhancing sensitivity to external stimuli like pressure and acceleration. Despite their usefulness, analyzing these inherently periodic structures poses significant computational challenges. In response, this paper presents a multiscale isogeometric analysis approach tailored for simulating piezoelectric materials. We introduce an electric–mechanical coupling model using isogeometric analysis (IGA) for two-dimensional piezoelectric membrane structures, assuming the plane stress hypothesis. Our proposed algorithm enables precise calculation of both displacement and electric potential solutions, demonstrating superior convergence properties compared to traditional finite element methods. Furthermore, we extend this approach to multiscale isogeometric analysis for computing numerical solutions in porous structures and heterogeneous composite piezoelectric materials under tensile and bending conditions. Through rigorous numerical testing, we evaluate the proposed extended multiscale isogeometric analysis method, showcasing its efficacy in achieving a balance between computational efficiency and simulation accuracy. This IGA-based electro-mechanical coupling model and numerical algorithm pave the way for more streamlined and precise simulations of piezoelectric materials within the context of flexible electronic devices. • Multi-scale simulation of piezoelectric material is carried out. • A mechanical–electric coupling formulation with EmsIGA is proposed. • Micro-scale units with smooth boundary are precisely described by IGA. [ABSTRACT FROM AUTHOR]

In this research, a framework of acoustic analysis and shape optimization, based on isogeometric boundary element method (IGA-BEM), is proposed for three-dimensional doubly periodic multilayered structures. The study addresses a gap in the literature by focusing on the shape optimization of such structures, which has not been extensively explored previously. The interface between different acoustic media is an infinite doubly periodic surface, which can be constructed by an open non-uniform rational B-splines. A periodic IGA-BEM is developed for the sound field analysis of the doubly periodic multilayered structure, in which the Ewald method is used to accelerate the calculation of periodic Green function. Furthermore, the shape derivative of the doubly periodic multiple boundaries is derived by imposing boundary perturbation and using the adjoint variable method. The control points of the NURBS surfaces are defined as the shape design variables, and all shape sensitivities can be quickly calculated by discretizing the shape derivative formula. Finally, in according with shape sensitivities, the corresponding shape optimization problem is solved by the method of moving asymptotes, so that the optimized shape design can be obtained. A series of numerical examples validates the accuracy and applicability of the proposed approaches. • A novel IGA-BEM is developed for the analysis of 3D doubly periodic multilayered acoustic structures. • The shape derivative formula is derived by boundary perturbation and the adjoint variable method. • The shape optimization is established for the doubly periodic acoustic structures. [ABSTRACT FROM AUTHOR]

• An isogeometric topology optimization (ITO) for maximizing band gaps was developed. • Both out-of-plane and in-plane wave modes optimization were considered. • The ITO method can widen band gaps with smooth optimized structures and fewer iterations. A smooth and efficient isogeometric topology optimization (ITO) method for maximizing band gaps in two-dimensional phononic crystals is developed in the paper. The band gaps of phononic crystals are computed by the NURBS-based isogeometric analysis, and the material distributions of two-dimensional phononic crystals are represented by the smooth, high-order continuity of the NURBS surface. The densities defined at each control point of the NURBS surface are employed as optimized design variables. The isogeometric analysis optimization using the same spline technique for both geometry and numerical analysis can benefit the optimization procedure and obtain smooth optimized structures, which can be easily used in 3D printing. The maximizing band gaps of phononic crystals for both out-of-plane and in-plane wave modes are obtained here using the present ITO approach. Numerical examples validated the effectiveness and reliability of the ITO method in broadening the band gaps and finding the optimal phononic crystals. And the numerical results show that the smooth optimized structures are obtained with fewer iterations. [ABSTRACT FROM AUTHOR]

The development of Micro-Electro-Mechanical Systems (MEMS) and portable electronic devices have facilitated the application of energy harvesters in self-powered microelectromechanical devices. This work presents an explicit topology optimization framework for the design of multi-material flexoelectric composite structures. It aims to achieve flexoelectric energy harvesting structures with enhanced energy conversion efficiency by optimizing the distribution of elastic and flexoelectric materials concurrently. The proposed method utilizes a set of groups of moving morphable components (MMC) to characterize the distribution of flexoelectric and elastic materials. The influence of different material overlapping schemes is also investigated in this work. The combination of isogeometric analysis (IGA) and MMC enables an efficient solution of flexoelectric high-order partial differential equations (PDEs). Numerical examples and experiments verify the effectiveness of the proposed method. Compared to other methods, the component-based MMC method not only facilitates the formation of efficient structures, but also directly produces the geometric model required for manufacturing. [ABSTRACT FROM AUTHOR]

In the present work, the fracture analysis of functionally graded (FG) porous structure containing an edge cracked is carried out in the presence of different types of porosity distributions using extended isogeometric analysis (XIGA). Firstly, the different types of porosity distribution functions are mathematically modeled in the porous FG structure across the length of the domain. The effective properties of the porous FG structure are computed using power law. Also, an additional term of porosity is incorporated in the power law to include the effect of porosity in the FG structure. The effective properties are computed across the length of the structure in the presence of different types of porosity distributions. Further, a pre-existing crack is modeled in the domain to study its influence on the fracture behaviour of porous FG structure using XIGA. To validate the accuracy, the results for the non-porous FG structure are compared with the available results in the literature (with the analytical and numerical solution), and they are found in good agreement (percentage error in the range of 0.04–––1.78%). Moreover, the comparative study is performed to investigate the influence of different types of porosity distributions on the fracture behaviour of FG structure. [ABSTRACT FROM AUTHOR]