As an efficient molecular simulation method, the smoothed molecular dynamics (SMD) method introduces background mesh and mapping process into molecular dynamics (MD) procedure to suppress high‐frequency modes, so that a much larger time step than that of MD can be adopted. SMD method can achieve a nice overall accuracy, but local atomic disorders cannot be described very well with original SMD method

This work presents a hybrid shear‐flexible beam‐element, capable of capturing arbitrarily large inelastic displacements and rotations of planar frame structures with just one element per member. Following Reissner’s geometrically‐exact theory, the finite element problem is herein formulated within nonlinear programming principles, where the total potential energy is treated as the objective function

An efficient computational approach to stress‐constrained topology optimization is presented. Using a multigrid‐preconditioned Krylov solver for the state and adjoint problems, the number of Krylov iterations is reduced significantly by enforcing early termination of the iterative solves. The criterion for early termination is based on the convergence of the design sensitivities with respect to Krylov

In this paper, we introduce a least‐squares virtual element method for the convection‐diffusion‐reaction problem in mixed form. We use the H (div) virtual element and continuous virtual element to approximate the flux and the primal variables, respectively. The method allows for the use of very general polygonal meshes. Optimal order a priori error estimates are established for the flux and the primal

We present new methodologies for the numerical solution of problems of elastic scattering by open arcs in two dimensions. The algorithms utilize weighted versions of the classical elastic integral operators associated with Dirichlet and Neumann boundary conditions, where the integral weight accounts for (and regularizes) the singularity of the integral‐equation solutions at the open‐arc endpoints.

For finite strain plasticity with both anisotropic yield functions and anisotropic hyperelasticity, we use the Kröner‐Lee decomposition of the deformation gradient to obtain a differential‐algebraic system (DAE) in the semi‐implicit form and solve it by an implicit Richards on extrapolated method based on intermediate substeps. The source is here the right Cauchy‐Green tensor and the consistent Jacobian

In this article, the authors formulate elastoplastic problems as a coupled problem of the equilibrium equation and the yield condition at each material point, and develop a numerical procedure based on the block Newton method to solve the overall structure using the finite element discretization. For the integration of stress, the backward difference scheme is employed. In the conventional return mapping

Differing from the finite element method, most of mesh‐free methods are restricted to 2‐D problems owing to the difficulty in constructing 3‐D grids. But, for 3‐D elastic structures, this limitation could be effectively overcome when hierarchical models are employed. In the hierarchical models of elastic structures, only the in‐plane displacement field is needed to be approximated because the thickness‐wise

A polynomial based model in conjunction with dimensional reduction method are presented to perform cross‐sectional analysis and to determine strain distribution in composite tubes under bending loading. For beam structures with tubular cross‐section, the Variational Asymptotic Method (VAM) has been employed to decompose a 3‐D elasticity problem into a 2‐D cross‐sectional analysis and a 1‐D analysis

An immersed boundary method (IBM) has been developed to handle the solid body embedded flowfield simulation for compressible reactive flows, paving the way of application for a wide range of fluid–solid interaction problems. Previously, the Brinkman penalization method (BPM), originated from porous media flows, has been successfully used for incompressible Navier–Stokes equations by adding penalization

Additive manufacturing (AM) techniques have grown significantly in recent years due to their ability to produce designs almost impossible to obtain with standard production technologies. This growth has in turn led to increased demand for numerical simulation of additive processes. Unfortunately, such simulations are difficult from the computational point of view, since additive problems are characterized

This article presents an enhanced version of our previous work, hybrid nonuniform subdivision (HNUS) surfaces, to achieve optimal convergence rates in isogeometric analysis (IGA). We introduce a parameter λ ( 1 4 < λ < 1 ) to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid nonuniform subdivision (tHNUS). Thus, HUNS is a special case of tHNUS when λ = 1 2 . While

Multi‐objective optimization is used for optimizing a number of objectives simultaneously. Mostly, the optimization algorithms considered the previous iterative position to find the next position updates. The main intention of this research is to design and develop a new model to solve the computational complexity, and the resource allocation problem. Based on this perspective, the Taylor series model

An Iterative Flexibility‐based Component Mode Synthesis (IF‐CMS) is presented for the model reduction of partitioned structural dynamic systems via localized Lagrange multipliers. A distinct IF‐CMS feature is the inclusion of hierarchical residual flexibility at each iteration, resulting in considerably improved accuracy compared with the classical Craig‐Bampton (CB) CMS method. The present IF‐CMS

The quasicontinuum (QC) method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse‐grained elsewhere. Since the method was originally proposed to accelerate atomistic lattice simulations, its refinement criteria—that drive refining coarse‐grained regions and/or increasing fully‐resolved regions—are generally associated with quantities

A hybrid‐mixed exact geometry four‐node thermopiezoelectric solid‐shell element through the sampling surfaces (SaS) formulation is proposed. The SaS formulation is based on the choice of an arbitrary number of SaS within layers parallel to the middle surface and located at Chebyshev polynomial nodes in order to introduce the temperatures, displacements and electric potentials of these surfaces as basic

Complex geometric features of fracture networks contained in rock masses can be captured by digital images quickly and accurately. However, the continuous and discontinuous deformation simulation of rock masses directly based on digital images is still challenging. Based on the Numerical Manifold Method (NMM), a simple and efficient image‐based simulation method is developed for rock masses containing

In this article, we present the behavior of two‐mode phase field crystal (2MPFC) method under a concentration dependent deformation. A mixed finite element formulation is proposed for the 2MPFC method that solves a 10th‐order parabolic equation. Lithium concentration diffusion in the electrode particle is captured by the Cahn–Hilliard (CH) equation and the host electrode material, LixMn2O4 (LMO), which

The proposed contribution is dedicated to numerical methods for solving strongly coupled fluid–structure dynamic problems where the complexity of the structures and the reduced remaining fluid volume do not allow to handle their exact geometry. Porous approaches are preferred instead but it is mandatory to go beyond classical techniques to account for inertial and convective components of the flow

A spectral consistent starting procedure is proposed for the first‐order‐type A‐stable linear two‐step (LTS) time integration methods in structural dynamics analysis. The accuracy analysis for the LTS methods in structural dynamics is presented based on the first‐order model, which enables the algorithms in first‐order transient systems to be extended to structural dynamics under the umbrella of a

A general‐purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in‐plane periodicity that cannot be effectively treated by a conventional method, such as woven fabrics. The framework is a generalization of the “finite element squared” (or FE2) method in which a localized

A framework to perform quantification and reduction of uncertainties in a wind turbine numerical model using a global sensitivity analysis and a recursive Bayesian inference method is developed in this article. We explain how a prior probability distribution on the model parameters is transformed into a posterior probability distribution, by incorporating a physical model and real field noisy observations

In this work, aspects considering material modeling of electro‐mechanical coupling in fiber reinforced electro‐active polymers (EAP) and the corresponding finite element implementation are considered. We propose a constitutive model that takes into account the electro‐viscoelastic behavior of the isotropic matrix and the influence of unidirectional fibers on both the hyperelastic response and the viscous

The material point method (MPM) has demonstrated itself as an effective numerical method to simulate extreme events with large deformations including fracture problems. However, the traditional MPM encounters difficulties in simulating discontinuities due to its continuous nodal shape function. In this paper, The eXtended Material Point Method (XMPM) is proposed to simulate the 3D crack propagation

The growing number of scienti_c publications on Topology Optimization (TO) shows the great interest that this technique has generated in recent years. Among the di_erent methodologies for TO, this paper focuses on the well known Solid Isotropic Material Penalization (SIMP) method [1], broadly used because of its simple formulation and effciency. Even so, the SIMP method has certain drawbacks, namely:

The newly proposed nonlocal macro‐meso‐scale damage (NMMD) model is extended to dynamic cracking simulation. For this purpose, the framework of continuum damage mechanics and damage constitutive model are firstly described. The NMMD, where the meso‐scale damage is determined according to the deformation of material bond and then the macroscopic topologic damage is endowed with the weighted averaging

The aim of the present study is to present an effect boundary element method (BEM) for electroelastic analysis of ultrathin piezoelectric films/coatings. The troublesome nearly singular integrals, which are crucial in applying the BEM for thin‐structural problems, are calculated accurately by using a nonlinear coordinate transformation method. The advanced BEM presented requires no remeshing procedure

A generic energy‐conserving linear normal contact model for concave particles in the discrete element method (DEM) is presented in this article. It is derived based on a recently enhanced general energy‐conserving contact theory for arbitrarily shaped particles. A set of more effective evaluation schemes required in the model are also given, which shows that only the intersection boundary between two

We propose a novel robust topology optimization for designing acoustic devices that are effective for broadband sound waves. Here, we define the objective function as the weighted sum of the acoustic response to an incident wave consisting of a single frequency and its standard deviation (SD) against the frequency perturbation. By approximating the SD, under the assumption that the incident frequency

This article presents a free vibration analysis of laminated sandwich plates under various boundary conditions by using an efficient C0 eight‐node quadrilateral element. This new element is formulated based on the recently proposed layerwise model. The present model assumes an improved first‐order shear deformation theory for the face sheets while a higher‐order theory is assumed for the core maintaining

We present an intuitive geometrical framework for non‐intrusive model reduction. Based on simple low‐dimensional geometry that is easy to visualize and interpret, the approach enables one to predict model features a priori and explain them a posteriori. Two simple a priori methods for analyzing the suitability of non‐intrusive model reduction are consequently presented and discussed. As a natural consequence

The systematic and physics‐infused construction of a projection‐based reduced‐order model (ROM) shows the capability to replicate the original high‐dimensional system's dynamical evolution but with a fractional computational cost. However, certain nonlinear features and high‐frequency contributions may be lost throughout the aggressive order reduction. Thus, ROMs in a broad category of fluid dynamics

We apply a Hybridizable Discontinuous Galerkin (HDG) method to numerically solve two‐dimensional anisotropic poroelastic wave equations in the frequency domain given by Biot theory. The motivation for choosing HDG method comes from the complexity of the considered equations and the high number of unknowns. The HDG method possesses all the advantages of Discontinuous Galerkin method (hpadaptivity, accuracy

Motivated by recent advances in manufacturing, the design of materials is in the focal point of interest in the material research community. One of the critical challenges in this field is finding optimal material microstructure for a desired macroscopic response. This work presents a computational method for mesoscale‐level design of particulate composites for an optimal macroscale‐level response

The efficient solution of the systems of equations arising from coupled consolidation problems are a matter of concern worldwide. The fixed‐stress splitting scheme is an effective approach for solving these equations either in a sequential manner or as a preconditioner for a fully coupled approach. Recent studies show that it is possible to improve the rate of convergence of the fixed‐stress approach

In this work we propose, analyze, and demonstrate an adjoint‐based multilevel multifidelity Monte Carlo (MLMF) framework called FastUQ. The framework is based on the MLMF of Geraci et al. and uses the Inexpensive Monte Carlo (IMC) method of Ghate as low‐fidelity surrogate. The setup cost of IMC‐1 surrogate in FastUQ requires just the adjoint solution at the input mean whose computational cost is independent

We present a 2D high‐order and easily accessible immersed‐boundary adaptive Harmonic Polynomial Cell (IB‐AHPC) method to solve fully‐nonlinear wave‐structure interaction problems in marine hydrodynamics using potential‐ow theory. To reduce the total number of cells without losing accuracy, adaptive quad‐tree cell refinements are employed close to the free‐surface and structure boundaries. The present

A thermo‐elastic topology optimization with stress and temperature constraints is proposed to attack the complex multi‐physics problem in this paper. Based on the rational approximation of material properties (RAMP), the coupled equations of mechanic and temperature field are solved. Two optimization problems, volume minimization with temperature and stress constraints, and traditional compliance minimization

In this paper we focus on a meshfree formulation for the solution of time‐harmonic acoustic scattering problems and verify the stability of the procedure. The sound waves propagate in nonhomogeneous media, giving rise to discontinuities in the gradients of the pressure field across the interfaces between regions of different material properties. Meshfree methods usually do not reproduce accurately

Classical solution methods in fast Fourier transform‐based computational micromechanics operate on, either, compatible strain fields or equilibrated stress fields. By contrast, polarization schemes are primal‐dual methods whose iterates are neither compatible nor equilibrated. Recently, it was demonstrated that polarization schemes may outperform the classical methods. Unfortunately, their computational

This article presents a density‐based topology optimization method for designing three‐dimensional (3D) compliant mechanisms (CMs) and loadbearing structures with design‐dependent pressure loading. Instead of interface‐tracking techniques, the Darcy law in conjunction with a drainage term is employed to obtain pressure field as a function of the design vector. To ensure continuous transition of pressure

Compliant mechanisms with multiple inputs and multiple outputs have a wide range of applications in precision mechanics, e.g., cell manipulations, electronic microscopes, and etc. The movement uncoupling and maximum desired output displacements among these devices all become critical because many inputs and outputs are involved. The topology optimization design of compliant mechanisms, which can solve

The natural fracture system plays an important role in the development of naturally fractured reservoirs. Traditionally, those reservoirs are simulated using dual‐porosity and dual‐permeability models. Conventional dual‐porosity models adopt over‐simplifications in terms of characterization of the fractured system. Generally, they focus on the hydraulic problem and do not consider the rock and fracture

The shakedown load of elastoplastic structures under multiple variable loading is an important factor in structural design and integrity analysis. In classical plasticity shakedown analysis is an essential and challenging problem. Most existing methods are based on the solution of super large‐scale mathematical programming, basis reduction or mechanics insight method which have their own limitations

A hybrid level set method is proposed for devising structures with embedded components, where the supporting structure as well as the positions and orientations of the components are optimized simultaneously. Two different types of level sets, namely the explicit and implicit level set are introduced to respectively represent the components and supporting structure. In this fashion, smooth geometries

We consider the problem of extracting a few desired eigenpairs of the buckling eigenvalue problem Kx = λKGx, where K is symmetric positive semi‐definite, KG is symmetric indefinite, and the pencil K –λKG is singular, namely, K and KG share a non‐trivial common nullspace. Moreover, in practical buckling analysis of structures, bases for the nullspace of K and the common nullspace of K and KG are available

This contribution presents the extensions of beam‐to‐beam and beam‐inside‐beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams' true surfaces (instead of surfaces implicitly deduced from the beams' centroid lines), the presented enhancements are not only able to account for frictional sliding in the beams' axial directions, but also in the

A topology optimization schema employing a condensation method for nonlinear frame structures with supplemental mass subjected to time‐varying excitation is presented. In the context of the design of structural frames, in certain applications, the supplemental mass can be order(s) of magnitude larger than the mass of the system itself. Thus, condensing the system of governing equations to only those

The hierarchical multiscale analysis normally utilizes a microscopic representative volume element (RVE) model to capture path/history‐dependent macroscopic responses instead of using phenomenological constitutive models. However, for problems involving large deformation, the current RVE model used in geomechanics may lose representative properties due to the progressive distortion of the RVE box,

Traditional reliability analysis is based on probability theory with precise distributions. However, determining the distribution of all variables precisely is impossible due to insufficient information. Therefore, random and interval variables may be encountered, and probabilistic reliability methods are hard to use. The existing interval variables make reliability analysis more difficult. In this

The enhanced assumed strain (EAS) method is one of the most frequently used methods to avoid locking in solid and structural finite elements. One issue of EAS elements in the context of geometrically nonlinear analyses is their lack of robustness in the Newton–Raphson scheme, which is characterized by the necessity of small load increments and large number of iterations. In the present work we extend

This article proposes an uncertainty‐oriented double‐scale topology optimization method considering macroreliability limitation and micromanufacturing control. The procedure combines the homogenization method to solve the equivalent elastic property of the microstructure, the feature distance theory to evaluate reliability, a density projection for manufacturability control, and the solid isotropic

A C1‐continuous time‐domain spectral finite element (SFE) is developed for efficient and accurate analysis of flexural‐guided wave propagation in Euler–Bernoulli beam‐type structures. A new C1‐continuous spectral interpolation using the Lobatto basis is proposed, which is shown to eliminate the Runge phenomenon observed in the conventional higher order Hermite interpolation. It is also able to diagonalize

Owing to the variations in geometric dimensions, material properties and external loads in engineering applications, robust topology optimization (RTO) has garnered increasing attention in recent years to account for the uncertain behaviors during the preliminary concept design phases. This paper presents a hybrid RTO method to simultaneously resolve the epistemic and aleatory uncertainties. First

The design of adaptive structures is one method to improve sustainability of buildings. Adaptive structures are able to adapt to different loading and environmental conditions or to changing requirements by either small or large shape changes. In the latter case, also the mechanics and properties of the deformation process play a role for the structure’s energy efficiency. The method of variational

The identification of hidden conducting permeable objects from measurements of the perturbed magnetic field taken over a range of low frequencies is important in metal detection. Applications include identifying threat items in security screening at transport hubs, location of unexploded ordnance, and antipersonnel landmines in areas of former conflict, searching for items of archeological significance

A numerical model for corrosion pit propagation under mechanical loading is presented. The level set method is used for corrosion front tracking and also enables the domain to be split into a solid and a pit domain. In the pit the diffusion of atoms originating from the dissolution process occurring at the pit front is simulated. The model is capable of automatically capturing lacy cover formation

In Jaśkowiec and Sukumar (Int J Numer Methods Eng, doi: 10.1002/nme.6528, 2020), we presented high‐order (p = 2–20) symmetric cubatures rules for tetrahedra and pyramids. This algorithm was sensitive to the initial location of the cubature nodes, and it did not converge for p > 11 over prisms and hexahedra (cubes). In this addendum, we resolve this issue and obtain high‐order symmetric rules over prisms

Due to simplicity in implementation and data structure, elements with equal‐order interpolation of velocity and pressure are very popular in finite‐element‐based flow simulations. Although such pairs are inf‐sup unstable, various stabilization techniques exist to circumvent that and yield accurate approximations. The most popular one is the pressure‐stabilized Petrov–Galerkin (PSPG) method, which consists

Additive manufacturing (AM) and topology optimization (TO) have a synergetic relation, as AM can produce complex TO designs, and TO provides high‐performance parts that utilize the form freedom provided by AM. Recently, TO has been tailored more toward AM with the inclusion of the minimum allowable overhang angle as a design constraint: resulting designs can be built without any support structures