This paper presents a novel method for topology optimization of vibrating structures interacted with acoustic wave for the purpose of minimizing radiated sound power level. We consider exterior acoustic fields and bi-material shell models without damping in this work. Within the isogeometric analysis framework, we employ Catmull–Clark subdivision surfaces to construct geometries and discretize physical

A new indirect boundary integral equation method (IBIEM) is developed to solve the seismic wave scattering problem in a three-dimensional fluid-saturated layered half-space. Based on Biot's theory, the Green's functions of inclined circular loads in porous elastic layered half-space are firstly deduced. According to the single-layer potential theory, when establishing the scattered wave field, the

The strain gradient elasticity theory is adopted to capture the small-scale effect of micro/nanostructures to derive the governing equation by using Hamilton's principle. A mesh-free method on the basis of moving Kriging interpolation, of which shape function possesses C2 continuum, is developed to investigate the vibration of the strain gradient plate. Owing to the inherent Kronecker delta function

We investigated the performance of various moving least squares (MLS) approximation schemes in surface fitting and in a partial-differential-equations solver based on the meshless local Petrov-Galerkin (MLPG) method. A modified weight functions in the MLS approximation and the orthogonal basis functions-based MLS ensures the Kronecker delta property. Variants of the MLS were first compared for the

In this paper, a meshless discrete scheme based on the generalized finite difference method (GFDM) is proposed to solve the biharmonic interface problem. This scheme turns the interface problem to be two non-interface subproblems coupled with the interface conditions. The interface conditions act as the boundary conditions of the subproblems because the interface plays the role of their boundary. Therefore

Recent developments suggest the use of triply periodic minimal surfaces (such as the gyroid) as a possibility for bone tissue scaffold. Moreover, through functional gradients of cellular structures, the mechanical properties can be edited and enhanced to achieve the most efficient results. One of the main concerns when designing bone scaffold is avoiding stress shielding, which occurs when the Young’s

Plasma generated by hypersonic aerocraft is one of the research subjects in computational electromagnetics. When the aerocraft flies at an ultra-high speed in the near space, plasma sheath will be generated in the surroundings and it will trigger varying changes in aerocraft radar electromagnetic scattering properties. Plasma sheath brings about tremendous impacts on the communication between the aerocraft

This paper extends our recent work [1] to evaluate the elastic fields and effective modulus of a composite containing arbitrarily shaped inhomogeneities for both two-dimensional (2D) and three-dimensional (3D) problems. Based on Eshelby’s equivalent inclusion method (EIM), the material mismatch between inhomogeneities and matrix phases is represented with a continuously distributed eigenstrain on inclusions

In this study, we develop a coupled hydraulic fracturing model based on peridynamics, propose a contact-friction constitutive model, and establish a bond breaking criterion based on bond stress to explore hydraulic fracture propagation in jointed rock. Subsequently, we study the effects of fracturing fluid parameters (viscosity and pumping rate) on the fracture propagation behavior. Our results show

It is established that the new boundary element-free Galerkin method, namely the virtual boundary element-free Galerkin method (VBEFGM), using dual compactly supported radial basis function interpolation (CSRBFI) for 2D inhomogeneous heat conduction problems with variable heat sources, whose solutions are divided into homogeneous and particular solutions. The virtual loads of the homogeneous solutions

In this paper a practical numerical method for calculating the settlement response of piles embedded in multilayered soils is presented. Finite beam elements are used for the discretization of piles. The soil mass, which is considered as a semi-infinite or finite medium with each layer being elastic, homogeneous and isotropic, is modeled with the boundary element method and the Steinbrenner's approximation

This work presents a novel scheme to couple the Discrete Element Method (DEM) and the Boundary Element Method (BEM) for the multi-scale modelling in the time domain. The DEM can model discontinuous material at micro scale very well, but it cannot represent infinite domains. Hence, coupling with the BEM is proposed. A formulation employing the DEM and BEM in different subdomains of the same body is

This paper deals with uncertainty quantification of transcranial electric stimulation (TES) of realistic human head model. The head model taken from Visible Human Project consists of 9 subdomains: scalp, skull, CSF, grey matter, white matter, cerebellum, ventricles, jaw and tongue. The deterministic computation of quasi-static induced electric scalar potential features boundary element method (BEM)

In this paper, we study multiscale methods for piezocomposites. We consider a model of static piezoelectric problem that consists of deformation with respect to components of displacements and a function of electric potential. This problem includes the equilibrium equations, the quasi-electrostatic equation for dielectrics, and a system of coupled constitutive relations for mechanical and electric

The main aim of this article is to develop an efficient boundary element method (BEM) modeling of the fractional nonlinear generalized photo thermal stress wave propagation problems in the context of functionally graded (FG) anisotropic smart semiconductors. Due to nonlinearity, fractional order heat conduction and strongly anisotropy of mechanical properties, the governing equations system of such

In this paper, a composite transformation method is developed to evaluate the singular and nearly singular boundary integrals in the boundary element analysis for multilayer thin structures. The composite transformation method is implemented as follows: Firstly, a sinh transformation method is developed to eliminate the influence of nearly singular integrals in the multilayer thin-structural problem;

Combining the nonlocal properties of peridynamics and the viewpoint of material point rotation, a novel peridynamic model enriched with the rotation effects of material points is proposed. By considering the rotation of material points, the concept of rotational micropotential is introduced into this proposed peridynamic model. On this basis, the translational and rotational governing equations of

Radial basis function (RBF) has been accurately used for the spatial discretization to solve PDE problems. In this paper, a practical stabilization of the local formulation of the radial basis function (RBF) method is presented to solve the incompressible fluid flows with heat transport problems. To avoid the nonlinearity of the convective term, we include the modified method of characteristics to

This paper investigates the effectiveness of a new hybrid passive control system on the seismic response of an existing steel cable-stayed bridge considering the pounding effect. The proposed hybrid passive control system comprises a seismic isolator and a metallic damper. The bridge is located in a high seismic zone and has suffered several damages including the earthquake-induced pounding damage

Groundwater flow problems are generally solved using analytical or numerical methods. Though analytical solutions are exact and preferable, they are not available for complex field problems. Hence numerical methods such as Finite Element and Finite Difference methods are used to solve complex groundwater problems. These conventional mesh/ grid-based numerical methods need construction of a detailed

The mixture stress gradient theory of elasticity is conceived via consistent unification of the classical elasticity theory and the stress gradient theory within a stationary variational framework. The boundary-value problem associated with a functionally graded nano-bar is rigorously formulated. The constitutive law of the axial force field is determined and equipped with proper non-standard boundary

Prior to this study, an empirical formula has been proposed to evaluate origin intensity factors on the Dirichlet boundary. In this work, a simple empirical formula for obtaining origin intensity factors on the Neumann boundary is provided. As a result, origin intensity factors both on Dirichlet boundary and Neumann boundary could be directly achieved. It makes the numerical implementation of the singular

We present a method based on integrated radial basis function-finite difference for numerical solution of plane elastostatic equations which is a boundary value problem. The two-dimensional version of the governed equation is solved by the proposed method on various geometries such as the rectangular and irregular domains. In the current paper, one of our goals is to present an improved integrated

The inhomogeneous magneto-electro-elastic (MEE) coupling element-free Galerkin method (IMC-EFGM) is proposed for solving static behaviors of MEE structures. Plates made of homogeneous or inhomogeneous MEE materials are analyzed by IMC-EFGM, and the mechanical behaviors in different temperature fields are simulated. Displacement, magnetic potential and electric potential are studied using moving least

In this work, a quadtree-polygonal smoothed finite element method is proposed for adaptive consistent framework of phase field model on brittle fracture problems. A Smoothed Galerkin Weak form aided with the gradient smoothing technique is formulated to construct the variational formulations for both displacement and phase field. Staggered scheme is employed to solve the coupled phase and displacement

Transporting of nanomachines using the nanoplates has been acknowledged as an emerging frontier of nanotechnology over recent years. This paper investigates the aerodynamic response of a temperature-dependent functionally-graded composite nanoplate reinforced by wavy carbon nanotubes (FG-WCNTRC nanoplate) under a nanoparticle moving in a straight path exposed by air drag. The meshfree finite volume

The convergence and stability of the fully nonlinear simulation in a three-dimensional potential numerical wave tank is vulnerable along the time marching algorithm of the free surface, as integrating the boundary element's solution into the high-order time integration of the free surface can trigger the numerical instability in the material node approach. Although this matter was identified in some

This paper presents a meshless finite point method (FPM) for the numerical analysis of the fractional cable equation. A second-order time discrete scheme is proposed to approximate both integer-order and fractional-order time derivatives. Then, based on the stabilized moving least squares approximation and the meshless smoothed gradients, a new implementation of the FPM is provided to enhance the accuracy

In the study, in conjunction with perfectly matched layer (PML) analysis, an approach is proposed for the evaluation of complex derivatives directly in terms of complex stretching coordinates of points in PML. For doing this within the framework of generalized finite difference method (GFDM), a difference equation is formulated and presented, where both the function values and coordinates of data points

Computational electromagnetic problems require evaluating the electric and magnetic fields of the physical object under investigation, divided into elementary cells with a mesh. The partial element equivalent circuit (PEEC) method has recently received attention from academic and industry communities because it provides a circuit representation of the electromagnetic problem. The surface formulation

In the current work, the stable node-based smoothed radial point interpolation method (SNS-RPIM) was used to investigate the dynamic responses of magneto-electro-elastic (MEE) beams under hygrothermal environment with the generalized Newmark method. Based on the generalized smoothed Galerkin weak form and the gradient smoothing technique, the basic equations for hygro-thermo-magneto-electro-elastic

We present an efficient multilevel Monte Carlo (MLMC) method for the topology optimization of flexoelectric structures. A flexoelectric composite consisting of flexoelectric and purely elastic building blocks is investigated. The governing equations are solved by Non-Uniform Rational B-spline (NURBS)-based isogeometric analysis (IGA) exploiting its higher order continuity. Genetic algorithms (GA) based

Electrospinning is a technique used to fabricate fibrillar materials for different applications. Understanding this process allows companies to reduce efforts and to have better control of the variables present in this phenomenon. A mathematical model is described in this article for Newtonian, Giesekus, FENE-P, and Oldroyd-B approaches. This was done by using radial basis functions through a localized

Micromechanical systems (MEMS) based on electrostatic actuators are commonly involved in driving and actuating high-speed micro-structures. For this to be efficient, these micro-actuators must produce sufficient actuating force in order to achieve the required large strokes for such operations (usually in the order of tens of microns). However, this larger amount of displacement will require high actuation

The radial basis function interpolation is an effective method for approximation on scattered data. However, this interpolation method suffers from the contradiction between the accuracy and the numerical stability. With considering the distribution of the interpolation points, a bounded random shape variation scheme for the radial basis function is developed to circumvent the problem of numerical

The 2.5D approach is an efficient tool for the dynamic analysis of half-space with longitudinally invariant properties. In this paper, a newly formulated 2.5D version of the NURBS-based isogeometric analysis (IGA) and the scaled boundary IGA (SBIGA) is proposed for analyzing the bounded and unbounded domains, respectively, of a soil-tunnel system subjected to moving railway loads. The bounded domain

Fracture has significant effect on the production of hydrogen–carbon compound reservoirs. Underground fluid always flows through different spaces which involves different flow patterns. In this study, the embedded discrete fracture method (EDFM) to couple the flow in matrix and fracture is introduced. The Darcy flow is considered in fracture while the Pre-Darcy flow is employed in matrix. The model

In this paper, linear oblique wave incident to a thin arc-shaped permeable barrier and an array of permeable circular cylinders was studied analytically. Two unique research objectives of this work include, considering the thickness for permeable material and the wavefield inside surrounded region by the permeable structure. The conventional boundary element method (BEM) is used to solve the governing

A new extended isogeometric boundary element method (XIGABEM) formulation is proposed for simulating multiple fatigue crack propagation in two-dimensional domains. The classical use of NURBS in isogeometric formulations is further extended by repeated knot insertion to introduce a C−1 continuity within the approximation space as an elegant approach to representing geometrical discontinuities at crack

Thermal metamaterials are a class of artificial composite structures with special thermal conduction properties. Due to the existence of complex multi-phase materials arrangement and interfaces in the thermal metamaterials, an efficient and accurate numerical method is on-demand to predict their temperature distribution and performances. In this paper, we studied the edge-based smoothed finite element

This study presents an adaptive binary-tree element subdivision method (BTSM) to evaluate the volume integrals with continuous or discontinuous kernels to facilitate automatic and high-quality patch generation. The BTSM, an essential technique implemented in boundary integral formulations, was proposed to guarantee a successful well-shaped element subdivision under any circumstances, improve integration

Quadrilateral mesh is a commonly used mathematical cover for numerical manifold method (NMM). However, the NMM based on quadrilateral isoparametric mapping has some intrinsic shortcomings, which is revealed for the first time in this study. Therefore, a new NMM is established to overcome these drawbacks by adopting a quadrilateral area coordinate system. In the proposed NMM, the stiffness matrix can

The main objective in this work is to study an application of the B-spline approximations in the Least Squares Method recovery of the structural response for boundary value problems in some linear elastic systems. These responses were approximated before using polynomial bases in the Stochastic perturbation-based Boundary Element Method and now are replaced with second or third order B-spline functions

Formulations of an extra-degree-of-freedom (DOF) free extended isogeometric analysis (IGA) are presented in this study. The idea is achieved by reconstruction of the coefficients through a mesh-free-based local approximation, based on the framework of a generalized finite-element method. The enrichment functions are embedded in the mesh-free basis implicitly, resulting in an identical number of DOFs

In this paper, a new meshfree approach is proposed for the three-dimensional free vibration analysis of laminated composite elliptical and paraboloidal shells of revolution. The three-dimensional theory of elasticity has been applied to formulations for free vibration analysis of laminated composite elliptical and paraboloidal shells of revolution. The field function is approximated by a new Tchebychev-point

This study is devoted to the evaluation of dynamic impedance of the arch dam foundation embedded in a complex layered half-space. For this purpose, a modified scaled boundary finite element method (SBFEM) is developed for modeling the far field. In order to overcome the limits of scaling requirements of the original SBFEM, a scaled boundary transformation based on a scaling surface is developed, which

An efficient finite element method-boundary element method (FEM-BEM) is proposed for electromagnetic analysis of inhomogeneous objects. The problem domain is discretized and evaluated with FEM, and the BEM introduces a truncated boundary on the surface of the domain utilizing boundary integral equations (BIEs) technique. To guarantee the precision, much dense discretization is usually required when

An innovative generalized Layer-Wise (LW) approach is proposed for the modal analysis of anisotropic doubly-curved shells with an arbitrary shape by employing the Generalized Differential Quadrature (GDQ) method. The geometrical description of shell structures can be traced from both the differential geometry and mapping technique based on a proper definition of the blending functions. The kinematic

In this paper, the fictitious stress method (FSM) as a meshless technique is extended to solve problems with inhomogeneities. The Eshelby's equivalent inclusion theory is coupled with the FSM as a set of particular solutions. There is no domain discretization as analytical solutions for inclusions are employed. The coupling procedure is presented, and the solution is carried out either in a direct

Grouting is a typical HM (hydro-mechanical) coupling process between slurry and rock and widely used in underground engineering to reinforce the strength of fractured rock mass. In present work, based on numerical manifold method (NMM), an NMM-HM grouting model is proposed to investigate slurry flowing and analyze grouting efficiency. In this NMM-HM grouting model, the slurry flows in fractures and

The meshless numerical manifold method (MNMM) inherits two covers of the numerical manifold method. A mathematical cover is composed of nodes' influence domains and a physical cover consists of physical patches, which are produced through cutting mathematical cover by physical boundaries. Because two covers are adopted, MNMM can naturally and uniquely solve both the continuous and discontinuous problems

In this paper, the improved interpolating dimension splitting element-free Galerkin (IIDSEFG) method based on nonsingular weight functions is proposed to solve 3D wave equations. By utilizing the dimension splitting method (DSM), a 3D wave equation is divided into a series of 2D problems. For 2D wave equations, the improved interpolating moving least-squares (IIMLS) method based on nonsingular weight

An improved grain-based numerical manifold method (NMM) is developed to investigate deformation and damage of intact rocks at the meso‑scale. The grain boundaries are embedded into the numerical manifold method using a random Voronoi tessellation technique to approximate the microstructure of rocks at the meso‑scale. To enhance efficiency, an improved contact loop updating algorithm is proposed, which

The human annulus fibrosus (HAF) is the major component in response to external forces for the intervertebral disk (IVD), which maintains the stability and flexibility of human spine. It can be assumed to be an anisotropic nearly incompressible hyperelastic composite consisting of collagen fibers and matrix in the numerical simulations of biomechanics. However, due to the geometric complexity and material

The bending behaviour of systems of straight elastic beams at different scales is investigated by the well-posed stress-driven nonlocal continuum mechanics. An effective computational methodology, based on nonlocal two-noded finite elements, is developed in order to take accurately into account long-range interactions present in the whole structural domain. The idea consists in partitioning the beam

Efficient and accurate evaluation of free-surface Green's function is the key to hydrodynamic problems solved by boundary element method (BEM). However, so far, there is still no unified numerical method that can accurately approximate all kinds of free-surface Green's functions. In theory, machine learning can be used to approximate any function with high accuracy. In the present study, neural networks

By adopting the scaling functions of the B-spline wavelet on the interval (BSWI) as interpolation functions, a wavelet-based boundary element method (BEM) model is constructed to compute the band structures of two-dimensional photonic crystals (2D PCs), which are composed of square or triangular lattices with arbitrarily shaped inclusions. The boundary integral equations of both the matrix and inclusion

In this paper, the Fragile Points Method (FPM) has been extended to solve the two-dimensional hyperbolic telegraph equation with specified initial and boundary conditions. Based on a naturally partitioned domain with scattered nodes and the Voronoi Diagram, the discretized FPM equations are derived by a Galerkin weak-form in the spatial domain and a finite difference scheme in the time domain. For

The second moment of inertia of a continuous axisymmetric object with an arbitrary shape made of a nonhomogeneous material is usually calculated by dividing it into small domains. However, it is a burdensome process to specify the density of the small domains. In this paper, a technique of easily calculating the second moment of inertia of an axisymmetric nonhomogeneous material using boundary integral

In this research, a combination of the numerical manifold method (NMM) and boundary element method (BEM) is presented for solving plane elasticity problems to benefit from the advantages of both methods. For this goal, the domain of the problems is divided into two regions, each region is analyzed separately, and finally, equilibrium and compatibility conditions are controlled in the interface by the