Showing papers in "International Journal for Numerical Methods in Engineering in 2009"

Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities

Abstract: Gmsh is an open-source 3-D finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. This paper presents the overall philosophy, the main design choices and some of the original algorithms implemented in Gmsh. Copyright (C) 2009 John Wiley & Sons, Ltd.

Convergence, adaptive refinement, and scaling in 1D peridynamics

Abstract: We introduce here adaptive refinement algorithms for the non-local method peridynamics, which was proposed in (J. Mech. Phys. Solids 2000; 48:175–209) as a reformulation of classical elasticity for discontinuities and long-range forces. We use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected. We discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1D in the limit of the horizon going to zero. Continuous micromoduli lead to optimal rates of convergence independent of the grid used, while discontinuous micromoduli produce optimal rates of convergence only for uniform grids. Examples for static and dynamic elasticity problems in 1D are shown. The relative error for the static and dynamic solutions obtained using adaptive refinement are significantly lower than those obtained using uniform refinement, for the same number of nodes. Copyright © 2008 John Wiley & Sons, Ltd.

Immersed particle method for fluid–structure interaction

Abstract: A method for treating fluid-structure interaction of fracturing structures under impulsive loads is described. The coupling method is simple and does not require any modifications when the structure fails and allows fluid to flow through openings between crack surfaces. Both the fluid and the structure are treated by meshfree methods. For the structure, a Kirchhoff-Love shell theory is adopted and the cracks are treated by introducing either discrete (cracking particle method) or continuous (partition of unity-based method) discontinuities into the approximation. Coupling is realized by a master-slave scheme where the structure is slave to the fluid. The method is aimed at problems with high-pressure and low-velocity fluids, and is illustrated by the simulation of three problems involving fracturing cylindrical shells coupled with fluids.

A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements

Abstract: This paper presents a novel face-based smoothed finite element method (FS-FEM) to improve the accuracy of the finite element method (FEM) for three-dimensional (3D) problems. The FS-FEM uses 4-node tetrahedral elements that can be generated automatically for complicated domains. In the FS-FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements. The results demonstrated that the FS-FEM is significantly more accurate than the FEM using tetrahedral elements for both linear and geometrically non-linear solid mechanics problems. In addition, a novel domain-based selective scheme is proposed leading to a combined FS/NS-FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The implementation of the FS-FEM is straightforward and no penalty parameters or additional degrees of freedom are used. The computational efficiency of the FS-FEM is found better than that of the FEM. Copyright © 2008 John Wiley & Sons, Ltd.

An efficient finite element method for embedded interface problems

Abstract: A stabilized finite element method based on the Nitsche technique for enforcing constraints leads to an efficient computational procedure for embedded interface problems. We consider cases in which the jump of a field across the interface is given, as well as cases in which the primary field on the interface is given. The finite element mesh need not be aligned with the interface geometry. We present closed-form analytical expressions for interfacial stabilization terms and simple procedures for accurate flux evaluations. Representative numerical examples demonstrate the effectiveness of the proposed methodology. Copyright © 2008 John Wiley & Sons, Ltd.

A method for interpolating on manifolds structural dynamics reduced‐order models

Abstract: A rigorous method for interpolating a set of parameterized linear structural dynamics reduced-order models (ROMs) is presented. By design, this method does not operate on the underlying set of parameterized full-order models. Hence, it is amenable to an online real-time implementation. It is based on mapping appropriately the ROM data onto a tangent space to the manifold of symmetric positive-definite matrices, interpolating the mapped data in this space and mapping back the result to the aforementioned manifold. Algorithms for computing the forward and backward mappings are offered for the case where the ROMs are derived from a general Galerkin projection method and the case where they are constructed from modal reduction. The proposed interpolation method is illustrated with applications ranging from the fast dynamic characterization of a parameterized structural model to the fast evaluation of its response to a given input. In all cases, good accuracy is demonstrated at real-time processing speeds. Copyright © 2009 John Wiley & Sons, Ltd.

Fast integration and weight function blending in the extended finite element method

Abstract: Two issues in the extended finite element method (XFEM) are addressed: efficient numerical integration of the weak form when the enrichment function is self-equilibrating and blending of the enrichment. The integration is based on transforming the domain integrals in the weak form into equivalent contour integrals. It is shown that the contour form is computationally more efficient than the domain form, especially when the enrichment function is singular and/or discontinuous. A method for alleviating the errors in the blending elements is also studied. In this method, the enrichment function is pre-multiplied by a smooth weight function with compact support to allow for a completely smooth transition between enriched and unenriched subdomains. A method for blending step function enrichment with singular enrichments is described. It is also shown that if the enrichment is not shifted properly, the weighted enrichment is equivalent to the standard enrichment. An edge dislocation and a crack problem are used to benchmark the technique; the influence of the variables that parameterize the weight function is analyzed. The resulting method shows both improved accuracy and optimum convergence rates and is easily implemented into existing XFEM codes

Hyper-reduction of mechanical models involving internal variables

Abstract: We propose to improve the efficiency of the computation of the reduced-state variables related to a given reduced basis. This basis is supposed to be built by using the snapshot proper orthogonal decomposition (POD) model reduction method. In the framework of non-linear mechanical problems involving internal variables, the local integration of the constitutive laws can dramatically limit the computational savings provided by the reduction of the order of the model. This drawback is due to the fact that, using a Galerkin formulation, the size of the reduced basis has no effect on the complexity of the constitutive equations. In this paper we show how a reduced-basis approximation and a Petrov-Galerkin formulation enable to reduce the computational effort related to the internal variables. The key concept is a reduced integration domain where the integration of the constitutive equations is performed. The local computations being not made over the entire domain, we extrapolate the computed internal variable over the full domain using POD vectors related to the internal variables. This paper shows the improvement of the computational saving obtained by the hyper-reduction of the elasto-plastic model of a simple structure

Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping

Abstract: This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.

Higher‐order XFEM for curved strong and weak discontinuities

Abstract: The extended finite element method (XFEM) enables the accurate approximation of solutions with jumps or kinks within elements. Optimal convergence rates have frequently been achieved for linear elements and piecewise planar interfaces. Higher-order convergence for arbitrary curved interfaces relies on two major issues: (i) an accurate quadrature of the Galerkin weak form for the cut elements and (ii) a careful formulation of the enrichment, which should preclude any problems in the blending elements. For (i), we employ a strategy of subdividing the elements into subcells with only one curved side. Reference elements that are higher-order on only one side are then used to map the integration points to the real element. For (ii), we find that enrichments for strong discontinuities are easily extended to higher-order accuracy. In contrast, problems in blending elements may hinder optimal convergence for weak discontinuities. Different formulations are investigated, including the corrected XFEM. Numerical results for several test cases involving strong or weak curved discontinuities are presented. Quadratic and cubic approximations are investigated. Optimal convergence rates are achieved using the standard XFEM for the case of a strong discontinuity. Close-to-optimal convergence rates for the case of a weak discontinuity are achieved using the corrected XFEM. Copyright © 2009 John Wiley & Sons, Ltd.

Piecewise constant level set method for structural topology optimization

Abstract: In this paper, a piecewise constant level set (PCLS) method is implemented to solve a structural shape and topology optimization problem. In the classical level set method, the geometrical boundary of the structure under optimization is represented by the zero level set of a continuous level set function, e.g. the signed distance function. Instead, in the PCLS approach the boundary is described by discontinuities of PCLS functions. The PCLS method is related to the phase-field methods, and the topology optimization problem is defined as a minimization problem with piecewise constant constraints, without the need of solving the Hamilton-Jacobi equation. The result is not moving the boundaries during the iterative procedure. Thus, it offers some advantages in treating geometries, eliminating the reinitialization and naturally nucleating holes when needed. In the paper, the PCLS method is implemented with the additive operator splitting numerical scheme, and several numerical and procedural issues of the implementation are discussed. Examples of 2D structural topology optimization problem of minimum compliance design are presented, illustrating the effectiveness of the proposed method.

Development and application of reduced-order modeling procedures for subsurface flow simulation

Abstract: The optimization of subsurface flow processes is important for many applications, including oil field operations and the geological storage of carbon dioxide. These optimizations are very demanding computationally due to the large number of flow simulations that must be performed and the typically large dimension of the simulation models. In this work, reduced-order modeling (ROM) techniques are applied to reduce the simulation time of complex large-scale subsurface flow models. The procedures all entail proper orthogonal decomposition (POD), in which a high-fidelity training simulation is run, solution snapshots are stored, and an eigen-decomposition (SVD) is performed on the resulting data matrix. Additional recently developed ROM techniques are also implemented, including a snapshot clustering procedure and a missing point estimation technique to eliminate rows from the POD basis matrix. The implementation of the ROM procedures into a general-purpose research simulator is described. Extensive flow simulations involving water injection into a geologically complex 3D oil reservoir model containing 60 000 grid blocks are presented. The various ROM techniques are assessed in terms of their ability to reproduce high-fidelity simulation results for different well schedules and also in terms of the computational speedups they provide. The numerical solutions demonstrate that the ROM procedures can accurately reproduce the reference simulations and can provide speedups of up to an order of magnitude when compared with a high-fidelity model simulated using an optimized solver. Copyright © 2008 John Wiley & Sons, Ltd.

A semi‐discrete shell finite element for textile composite reinforcement forming simulation

Abstract: A triangular shell element for the simulation of textile composite reinforcements forming is proposed. This element is made up of unit woven cells. The internal virtual works are added on all woven cells of the element. They depend on tensions, in-plane shear and bending moments that are directly those given by the experimental tests that are specific to textile composite reinforcement. The element has only displacement degrees of freedom; the bending curvatures are obtained from the displacement of the neighbouring elements. A set of example shows the efficiency of the approach and the relative roles of the tensile, in-plane shear and bending rigidities. Especially their influence on the appearance and the development of wrinkles in draping and forming tests is analysed. Copyright © 2009 John Wiley & Sons, Ltd.

Level set topology optimization of fluids in Stokes flow

Abstract: We propose the level set method of topology optimization as a viable, robust and efficient alternative to density‐based approaches in the setting of fluid flow. The proposed algorithm maintains the discrete nature of the optimization problem throughout the optimization process, leading to significant advantages over density‐based topology optimization algorithms. Specifically, the no‐slip boundary condition is implemented directly—this is accurate, removes the need for interpolation schemes and continuation methods, and gives significant computational savings by only requiring flow to be modeled in fluid regions. Topological sensitivity information is utilized to give a robust algorithm in two dimensions and familiar two‐dimensional power dissipation minimization problems are solved successfully. Computational efficiency of the algorithm is also clearly demonstrated on large‐scale three‐dimensional problems.

A dissipation-based arc-length method for robust simulation of brittle and ductile failure

Abstract: A robust method to trace the equilibrium path in non-linear solid mechanics problems is proposed. A general arc-length constraint based on the energy release rate is developed. Constraints have been derived for the cases of geometrically linear damage, geometrically linear plasticity and geometrically non-linear damage. All three constraints can efficiently be applied in a finite element context. Numerical simulations demonstrate that the proposed framework gives robust results for these cases. Applicability of the proposed framework to other types of constitutive and/or kinematic behaviour is predicted.

A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method

Abstract: This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to earlier approaches. we do not work with an interior penalty formulation as, e.g. for Nitsche techniques, but impose the constraints weakly in terms of Lagrange multipliers. Roughly speaking a stable and optimal discrete Lagrange multiplier space has to satisfy two criteria: a best approximation property and a uniform inf-sup condition. Owing to the fact that the interface does not match the edges of the mesh, the choice of a good discrete Lagrange Multiplier space is not trivial. Here we propose a new algorithm for the local construction of the Lagrange Multiplier space and show that a uniform inf-sup condition is satisfied. A counterexample is also presented, i.e. the inf-sup constant depends on the mesh-size and degenerates as it tends to zero. Numerical results in two-dimensional confirm the theoretical ones. Copyright

SPH with the multiple boundary tangent method

Abstract: In this article, we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics (SPH) method. Benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries. As well, current SPH boundary approaches do not properly treat curved boundaries in complicated flow domains. These drawbacks have been remedied in a new boundary treatment method presented in this article, called the multiple boundary tangent (MBT) approach. In this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions. The two benchmark problems chosen are the lid-driven cavity problem, and flow over a cylinder. The SPH solutions using the MBT approach and the results from literature are in very good agreement. These solutions involved solid boundaries, but the approach presented herein should be extendable to time-evolving, free-surface boundaries.

Vibrations of an elastic structure with shunted piezoelectric patches: efficient finite element formulation and electromechanical coupling coefficients

Abstract: This article is devoted to the numerical simulation of the vibrations of an elastic mechanical structure equipped with several piezoelectric patches, with applications for the control, sensing and reduction of vibrations. At first, a finite element formulation of the coupled electromechanical problem is introduced, whose originality is that provided a set of non-restrictive assumptions, the system's electrical state is fully described by very few global discrete unknowns: only a couple of variables per piezoelectric patches, namely (1) the electric charge contained in the electrodes and (2) the voltage between the electrodes. The main advantages are (1) since the electrical state is fully discretized at the weak formulation step, any standard (elastic only) finite element formulation can be easily modified to include the piezoelectric patches (2) realistic electrical boundary conditions such that equipotentiality on the electrodes and prescribed global charges naturally appear (3) the global charge/voltage variables are intrinsically adapted to include any external electrical circuit into the electromechanical problem and to simulate shunted piezoelectric patches. The second part of the article is devoted to the introduction of a reduced-order model (ROM) of the problem, by means of a modal expansion. This leads to show that the classical efficient electromechanical coupling factors (EEMCF) naturally appear as the main parameters that master the electromechanical coupling in the ROM. Finally, all the above results are applied in the case of a cantilever beam whose vibrations are reduced by means of a resonant shunt. A finite element formulation of this problem is described. It enables to compute the system EEMCF as well as its frequency response, which are compared with experimental results, showing an excellent agreement.

Octree‐based reasonable‐quality hexahedral mesh generation using a new set of refinement templates

Abstract: An octree-based mesh generation method is proposed to create reasonable-quality, geometry-adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features A new, easy-to-implement, easy-to-understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creating hanging nodes A buffer layer is inserted on an octree core mesh to improve the mesh quality significantly Laplacian-like smoothing, angle-based smoothing and local optimization-based untangling methods are used with certain restrictions to further improve the mesh quality Several examples are shown to demonstrate the capability of our hexahedral mesh generation method for complex geometries Copyright © 2008 John Wiley & Sons, Ltd

A boundary face method for potential problems in three dimensions

Abstract: This work presents a new implementation of the boundary node method (BNM) for numerical solution of Laplace's equation. By coupling the boundary integral equations and the moving least-squares (MLS) approximation, the BNM is a boundary-type meshless method. However, it still uses the standard elements for boundary integration and approximation of the geometry, thus loses the advantages of the meshless methods. In our implementation, here called the boundary face method, the boundary integration is performed on boundary faces, which are represented in parametric form exactly as the boundary representation data structure in solid modeling. The integrand quantities, such as the coordinates of Gauss integration points, Jacobian and out normal are calculated directly from the faces rather than from elements. In order to deal with thin structures, a mixed variable interpolation scheme of 1-D MLS and Lagrange Polynomial for long and narrow faces. An adaptive integration scheme for nearly singular integrals has been developed. Numerical examples show that our implementation can provide much more accurate results than the BNM, and keep reasonable accuracy in some extreme cases, such as very irregular distribution of nodes and thin shells. Copyright © 2009 John Wiley & Sons, Ltd.

Reliability sensitivity analysis with random and interval variables

Abstract: In reliability analysis and reliability-based design, sensitivity analysis identifies the relationship between the change in reliability and the change in the characteristics of uncertain variables. Sensitivity analysis is also used to identify the most significant uncertain variables that have the highest contributions to reliability. Most of the current sensitivity analysis methods are applicable for only random variables. In many engineering applications, however, some of uncertain variables are intervals. In this work, a sensitivity analysis method is proposed for the mixture of random and interval variables. Six sensitivity indices are defined for the sensitivity of the average reliability and reliability bounds with respect to the averages and widths of intervals, as well as with respect to the distribution parameters of random variables. The equations of these sensitivity indices are derived based on the first-order reliability method (FORM). The proposed reliability sensitivity analysis is a byproduct of FORM without any extra function calls after reliability is found. Once FORM is performed, the sensitivity information is obtained automatically. Two examples are used for demonstration. Copyright © 2009 John Wiley & Sons, Ltd.

A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Geometrically linear problems

Abstract: In this paper a new reduced integration eight-node solid-shell finite element is presented. The enhanced assumed strain (EAS) concept based on the Hu-Washizu variational principle requires only one EAS degree-of-freedom to cure volumetric and Poisson thickness locking. One key point of the derivation is the Taylor expansion of the inverse Jacobian with respect to the element center, which closely approximates the element shape and allows us to implement the assumed natural strain (ANS) concept to eliminate the curvature thickness and the transverse shear locking. The second crucial point is a combined Taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization without rank deficiency. Hence, the element requires only a single integration point in the shell plane and at least two integration points in thickness direction. The formulation fulfills both the membrane and the bending patch test exactly, which has, to the authors' knowledge, not yet been achieved for reduced integration eight-node solid-shell elements in the literature. Owing to the three-dimensional modeling of the structure, fully three-dimensional matenal models can be implemented without additional assumptions.

A finite deformation mortar contact formulation using a primal–dual active set strategy

Abstract: In recent years, nonconforming domain decomposition techniques and in particular the mortar method have become popular in developing new contact algorithms. Here, we present an approach for two-dimensional frictionless multibody contact based on a mortar formulation and using a primal-dual active set strategy for contact constraint enforcement. We consider linear and higher order (quadratic) interpolations throughout this work. So-called dual Lagrange multipliers are introduced for the contact pressure but can be eliminated from the global system of equations by static condensation, thus avoiding an increase in system size. For this type of contact formulation, we provide a full linearization of both contact forces and normal (non-penetration) and tangential (frictionless sliding) contact constraints in the finite deformation frame. The necessity of such a linearization in order to obtain a consistent Newton scheme is demonstrated. By further interpreting the active set search as a semi-smooth Newton method, contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme. This yields a robust and highly efficient algorithm for frictionless finite deformation contact problems. Numerical examples illustrate the efficiency of our method and the high quality of results.

An unfitted finite element method using discontinuous Galerkin

Abstract: In this paper we present a new approach to simulations on complex-shaped domains. The method is based on a discontinuous Galerkin (DG) method, using trial and test functions defined on a structured grid. Essential boundary conditions are imposed weakly via the DG formulation. This method offers a discretization where the number of unknowns is independent of the complexity of the domain. We will show numerical computations for an elliptic scalar model problem in ℝ 2 and ℝ 3 . Convergence rates for different polynomial degrees are studied.

The extended finite element method for fracture in composite materials

Abstract: Methods for treating fracture in composite material by the extended finite element method with meshes that are independent of matrix/fiber interfaces and crack morphology are described. All discontinuities and near-tip enrichments are modeled using the framework of local partition of unity. Level sets are used to describe the geometry of the interfaces and cracks so that no explicit representation of either the cracks or the material interfaces are needed. Both full 12 function enrichments and approximate enrichments for bimaterial crack tips are employed. A technique to correct the approximation in blending elements is used to improve the accuracy. Several numerical results for both two-dimensional and three-dimensional examples illustrate the versatility of the technique. The results clearly demonstrate that interface enrichment is sufficient to model the correct mechanics of an interface crack. Copyright © 2008 John Wiley & Sons, Ltd.

The scaled boundary finite element method in structural dynamics

Abstract: The scaled boundary finite element method is extended to solve problems of structural dynamics. The dynamic stiffness matrix of a bounded (finite) domain is obtained as a continued fraction solution for the scaled boundary finite element equation. The inertial effect at high frequencies is modeled by high-order terms of the continued fraction without introducing an internal mesh. By using this solution and introducing auxiliary variables, the equation of motion of the bounded domain is expressed in high-order static stiffness and mass matrices. Standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain. Numerical examples for modal and direct time-domain analyses are presented. Rapid convergence is observed as the order of continued fraction increases. A guideline for selecting the order of continued fraction is proposed and validated. High computational efficiency is demonstrated for problems with stress singularity.

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Abstract: SUMMARY Based on the differential quadrature (DQ) rule, the Gauss Lobatto quadrature rule and the variational principle, a DQ finite element method (DQFEM) is proposed for the free vibration analysis of thin plates. The DQFEM is a highly accurate and rapidly converging approach, and is distinct from the differential quadrature element method (DQEM) and the quadrature element method (QEM) by employing the function values themselves in the trial function for the title problem. The DQFEM, without using shape functions, essentially combines the high accuracy of the differential quadrature method (DQM) with the generality of the standard finite element formulation, and has superior accuracy to the standard FEM and FDM, and superior efficiency to the p-version FEM and QEM in calculating the stiffness and mass matrices. By incorporating the reformulated DQ rules for general curvilinear quadrilaterals domains into the DQFEM, a curvilinear quadrilateral DQ finite plate element is also proposed. The inter-element compatibility conditions as well as multiple boundary conditions can be implemented, simply and conveniently as in FEM, through modifying the nodal parameters when required at boundary grid points using the DQ rules. Thus, the DQFEM is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter-element compatibilities. A series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the DQFEM. Copyright q 2009 John Wiley & Sons, Ltd.

Uncertainty quantification in chemical systems

Abstract: SUMMARY We demonstrate the use of multiwavelet spectral polynomial chaos techniques for uncertainty quantification in non-isothermal ignition of a methane–air system. We employ Bayesian inference for identifying the probabilistic representation of the uncertain parameters and propagate this uncertainty through the ignition process. We analyze the time evolution of moments and probability density functions of the solution. We also examine the role and significance of dependence among the uncertain parameters. We finish with a discussion of the role of non-linearity and the performance of the algorithm. Copyright q 2009 John Wiley & Sons, Ltd.

Recent advances on the use of separated representations

Abstract: Separated representations based on finite sum decompositions constitute an appealing strategy for reducing the computer resources and the calculation costs by reducing drastically the number of degrees of freedom that the functional approximations involve (the number of degrees of freedom scale linearly with the dimension of the space in which the model is defined instead of the exponential growing characteristic of mesh-based discretization strategies). In our knowledge the use of separated representations is the only possibility for circumventing the terrific curse of dimensionality related to some highly multidimensional models involving hundreds of dimensions, as we proved in some of our former works. Its application is not restricted to multidimensional models, obviously separated representation can also be applied in standard 2D or 3D models, allowing for high resolution computations. Because its early life numerous issues persist, many of them attracting the curiosity of many research groups within the computational mechanics community. In this paper we are focusing in two issues never until now addressed: (i) the imposition of non-homogenous essential boundary conditions and (ii) the consideration of complex geometries. Copyright © 2009 John Wiley & Sons, Ltd.

Integrated layout design of multi‐component system

Abstract: A new integrated layout optimization method is proposed here for the design of multi-component systems. By introducing movable components into the design domain, the components layout and the supporting structural topology are optimized simultaneously. The developed design procedure mainly consists of three parts: (i) Introduction of non-overlap constraints between components. The finite circle method (FCM) is used to avoid the components overlaps and also overlaps between components and the design domain boundaries. (ii) Layout optimization of the components and supporting structure. Locations and orientations of the components are assumed as geometrical design variables for the optimal placement while topology design variables of the supporting structure are defined by the density points. Meanwhile, embedded meshing techniques are developed to take into account the finite element mesh change caused by the component movements. (iii) Consistent material interpolation scheme between element stiffness and inertial load. The commonly used solid isotropic material with penalization model is improved to avoid the singularity of localized deformation in the presence of design dependent loading when the element stiffness and the involved inertial load are weakened by the element material removal. Finally, to validate the proposed design procedure, a variety of multi-component system layout design problems are tested and solved on account of inertia loads and gravity center position constraint. Solutions are compared with traditional topology designs without component. Copyright © 2008 John Wiley & Sons, Ltd.