Automatic generation of quadrilateral finite element meshes

This paper describes an efficient, accurate and simple implementation of an algorithm for generation of quadrilateral finite element meshes. An original algorithm by Talbert and Parkinson [J.A. Talbert, A. Parkinson, Development of an automatic two-dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition, Int. J. Numer. Meth. Eng., 29 (1990) 1551–1567], has been substantially redeveloped and modified and presented in greater detail. We cover several important issues omitted in publication mentioned and we will provide interested readers with fully documented source code of the program.     

Image-based finite element mesh construction for material microstructures

One way of computing the macroscopic behavior of a material sample with complex microstructure is to construct a finite element model based on a micrograph of a representative slice of the material. The quality of the results produced with such a model obviously depends on the quality of the constructed mesh. In this article, we describe a set of routines that modify and improve the quality of a 2D mesh. Most of the routines are guided by an effective element “energy” functional, which takes into account the shape quality of the elements and the homogeneity of the elements as determined from an underlying segmented image. The interfaces and boundaries in the image arise naturally from the segmentation process. From these routines, we construct a close-to-automatic mesh generator that requires only a few inputs, such as the linear sizes of the largest and smallest features in the micrograph.     

Iterative mesh partitioning optimization for parallel nonlinear dynamic finite element analysis with direct substructuring

 This work presents a novel iterative approach for mesh partitioning optimization to promote the efficiency of parallel nonlinear dynamic finite element analysis with the direct substructure method, which involves static condensation of substructures' internal degrees of freedom. The proposed approach includes four major phases – initial partitioning, substructure workload prediction, element weights tuning, and partitioning results adjustment. The final three phases are performed iteratively until the workloads among the substructures are balanced reasonably. A substructure workload predictor that considers the sparsity and ordering of the substructure matrix is used in the proposed approach. Several numerical experiments conducted herein reveal that the proposed iterative mesh partitioning optimization often results in a superior workload balance among substructures and reduces the total elapsed time of the corresponding parallel nonlinear dynamic finite element analysis. Received 22 August 2001 / Accepted 20 January 2002     

Mesh design in finite element analysis of post-buckled delamination in composite laminates

The role of mesh design in the post-buckling analysis of delamination in composite laminates is addressed in this paper. The determination of the strain energy release rate (SERR) along the crack front is central to the analysis. Frequently, theoretical analysis is limited to treatment of the problem in two dimensions, since considerable complexity is encountered in extending the analysis to three dimensions. However, many practical problems of embedded delamination in composite laminates are inherently three-dimensional in nature. Although in such cases, the finite element (FE) method can be employed, there are some issues that must be examined more closely to ensure physically realistic models. One of these issues is the effect of mesh design on the determination of the local SERR along the delamination front. There are few studies that deal with this aspect systematically. In this paper, the effect of mesh design in the calculation of SERR in two-dimensional (2D) and three-dimensional (3D) FE analyses of the post-buckling behavior of embedded delaminations is studied and some guidelines on mesh design are suggested. Two methods of calculation of the SERR are considered: the virtual crack closure technique (VCCT) and crack closure technique (CCT). The 2D analyses confirm that if the near-tip mesh is symmetric and consists of square elements, then the evaluation of the SERR is not sensitive to mesh refinement, and a reasonably coarse mesh is adequate. Despite agreement in the global post-buckling response of the delaminated part, the SERR calculated using different unsymmetrical near-tip meshes could be different. Therefore, unsymmetrical near-tip meshes should be avoided, as convergence of the SERR with mesh refinement could not be assured. While the results using VCCT and CCT for 2D analyses agree well with each other, these techniques yield different quantitative results when applied to 3D analyses. The reason may be due to the way in which the delamination growth is modeled. The CCT allows simultaneous delamination advance over finite circumferential lengths, but it is very difficult to implement and the results exhibit mesh dependency. Qualitatively, however, the two sets of results show similar distributions of Mode I and Mode II components of the SERR. This is fortunate, since the VCCT is relatively easy to implement.     

Investigation of finite element mesh independence in rate dependent materials

Crystal plasticity theory is commonly used in finite element analyses to predict large strain ductility in single crystal and polycrystal deformation. In the rate-dependent formulation of the theory it is possible, for cases of simple deformation, to achieve an analytical solution that is independent of any effects due to the finite element mesh spacing. In this study single crystal and polycrystal models were subjected to alternative loading conditions. The effect of the mesh density on the generation of strain localisations and shear bands was investigated with regard to consistency of results. It was found that, prior to the initiation of a narrow shear band, it was possible to achieve a numerical result independent of mesh spacing. In the larger polycrystal analyses, an element size was identified that enabled the generation of a mesh independent solution. This allowed the accurate prediction of the mechanical behaviour of the model up to, and including, the failure point. The implications of this for small-scale metallic device design are discussed.     

Automatic three-dimensional finite element mesh generation via modified ray casting

Three-dimensional (3-D) finite element mesh generation has been the target of automation due to the complexities associated with generating and visualizing the mesh. A fully automatic 3-D mesh generation method is developed. The method is capable of meshing CSG solid models. It is based on modifying the classical ray-casting technique to meet the requirements of mesh generation. The modifications include the utilization of the element size in the casting process, the utilization of 3-D space box enclosures, and the casting of ray segments (rays with finite length). The method begins by casting ray segments into the solid. Based on the intersections between the segments and the solid boundary, the solid is discretized into cells arranged in a structure. The cell structure stores neighbourhood relations between its cells. Each cell is meshed with valid finite elements. Mesh continuity between cells is achieved via the neighbourhood relations. The last step is to process the boundary elements to represent closely the boundary. The method has been tested and applied to a number of solid models. Sample examples are presented.     

Space adaptive finite element methods for dynamic Signorini problems

Space adaptive techniques for dynamic Signorini problems are discussed. For discretisation, the Newmark method in time and low order finite elements in space are used. For the global discretisation error in space, an a posteriori error estimate is derived on the basis of the semi-discrete problem in mixed form. This approach relies on an auxiliary problem, which takes the form of a variational equation. An adaptive method based on the estimate is applied to improve the finite element approximation. Numerical results illustrate the performance of the presented method. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

An object-oriented finite element framework for multiphysics phase field simulations

The phase field approach is a powerful and popular method for modeling microstructure evolution. In this work, advanced numerical tools are used to create a framework that facilitates rapid model development. This framework, called MARMOT, is based on Idaho National Laboratory’s finite element Multiphysics Object-Oriented Simulation Environment. In MARMOT, the system of phase field partial differential equations (PDEs) are solved simultaneously together with PDEs describing additional physics, such as solid mechanics and heat conduction, using the Jacobian-Free Newton Krylov Method. An object-oriented architecture is created by taking advantage of commonalities in the phase field PDEs to facilitate development of new models with very little effort. In addition, MARMOT provides access to mesh and time step adaptivity, reducing the cost for performing simulations with large disparities in both spatial and temporal scales. In this work, phase separation simulations are used to show the numerical performance of MARMOT. Deformation-induced grain growth and void growth simulations are also included to demonstrate the muliphysics capability.     

Tetrahedral mesh generation in convex primitives

This paper presents a method for generating tetrahedral meshes in three-dimensional primitives. Given a set of closed and convex polyhedra having non-zero volume and some mesh controlling parameters, the polyhedra are automatically split to tetrahedra satisfying the criteria of standard finite element meshes. The algorithm tries to generate elements close to regular tetrahedra by maximizing locally the minimum solid angles associated to a set of a few neighbouring tetrahedra. The input parameters define the size of the tetrahedra and they can be used to increase or decrease the discretization locally. All the new nodes, which are not needed to describe the geometry, are generated automatically.     

Three-dimensional finite element analysis of finite deformation micromorphic linear isotropic elasticity

A finite deformation micromorphic materially linear isotropic elastic model is formulated and implemented for three dimensional finite element analysis. The model is based on the kinematics, balance equations and thermodynamic equations proposed by Eringen and Suhubi (1964). The constitutive equations are calculated in the reference configuration, and the resulting stresses are mapped to the current configuration. The balance of linear momentum and the balance of first moment of momentum are linearized to construct the consistent tangent for three dimensional finite element implementation for solution by the Newton–Raphson method. Three dimensional numerical examples are analyzed to demonstrate preliminarily the implementation.     

Adaptive selection of polynomial degrees on a finite element mesh

The problem of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed. An a posteriori error estimator based on the minimum complementary energy principle is proposed which utilizes the displacement vector field computed from the finite element solution. This estimator, designed for p- and hp-extensions, is conceptually different from estimators based on residuals or patch recovery which are designed for h-extension procedures. The quality of the error estimator is demonstrated by examples. The results show that the effectivity index is reasonably close to unity and the sequences of p-distributions obtained with the error indicators closely follow the optimal trajectory. © 1998 John Wiley & Sons, Ltd.     

A complete finite element treatment for the fully coupled implicit ALE formulation

This paper presents a complete derivation and implementation of the Arbitrary Lagrangian Eulerian (ALE) formulation for the simulation of large deformation quasi-static and dynamic problems. While most of the previous work done on ALE for dynamic applications was mainly based on operator split and explicit calculations, this work derives the quasi-static and dynamic ALE equations using a fully coupled implicit approach. Full expression for the ALE virtual work equations and finite element matrices are given. Time integration relations for the dynamic equations are also derived. Several quasi-static and dynamic large deformation applications are solved and presented.     

Elasto-plastic finite element analysis of a crack in an infinite plate

The elastic support method was recently developed to simulate the effects of unbounded solids in the finite element analysis of stresses and displacements. The method eliminates all the computational disadvantages encountered in the use of `infinite' elements or coupled finite element boundary element methods while retaining all the computational advantages of the finite element method. In this paper, the method is extended to the elasto-plastic analysis of fracture in infinite solids by using the load increment approach and including the effects of strain hardening. Numerical tests and parametric study are conducted by analysing a straight crack in an infinite plate. Present results for J integrals and plastified zones are compared, respectively, with analytical solutions and available results obtained by using the body force method. The agreement between the results is found to be very good even if the truncation boundary of the finite element model is located very close to the crack tip or the plastified zone.     

From the individual element test to finite element templates: Evolution of the patch test

This paper starts a sequence of three articles that follow an unconventional approach in finite element research. The ultimate objective is to construct high-performance elements and element-level error estimators for those elements. The approach takes off from our previous work in high-performance elements and culminates with the development of finite element templates. The present paper concentrates on the patch test and evolved versions of the test that have played a key role in this research. Following a brief review of the historical roots, we present the Individual Element Test (IET) of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements. The relationship of the IET to the multielement forms A, B and C of the patch test and to the single-element test are investigated. An important consequence of the IET application is that the element stiffness equations decompose naturally into basic and higher-order parts. The application of this decomposition to the “sanitization” of the non-convergent BCIZ element is described and verified with numerical experiments. Two sequel papers in preparation are subtitled ‘the algebraic approach’ and ‘element-level error estimation’. These apply the fundamental decomposition to the derivation of templates for specific mechanical elements and to the construction of element-level error estimators, respectively.     

Thermomechanical finite element simulations of ultrasonically assisted turning

Ultrasonically assisted turning (UAT) is studied with finite element (FE) simulations and compared with conventional turning (CT) using both computational results and infrared thermography experiments. The two-dimensional thermomechanically coupled FE model of both UAT and CT utilizes MSC MARC general FE code and incorporates temperature dependent material properties, strain rate effects, heat generated due to plastic flow, contact interaction and friction at the cutter/workpiece interface. Material separation in front of a cutting edge and automatic remeshing of distorted elements are implemented in the developed computational scheme. Influence of friction on resultant temperatures and chip shapes in turning for both UAT and CT is discussed. Temperature fields in the cutting region and in the cutting tool for CT and UAT are studied and compared with the experimental data. A role of various heat transfer parameters on thermal processes in UAT and CT is investigated.     

Multiscale finite element modeling of superelasticity in Nitinol polycrystals

An efficient method is proposed for modeling superelastic polycrystalline NiTi by solving a two-scale problem. The RVE size of the fine scale is determined using a statistics-based approach. Both problems are discretized in space using the finite element method and their communication is effected using MPI. Representative simulations illustrate the modeling capabilities of the proposed approach.     

Determination of residual stresses in welded components by finite element analysis

The continued safe and reliable operation of plant invariably has to consider the assessment of defects in welded structural components. This requires some estimate of the residual stresses that have developed during the welding fabrication process. There is an increasing use of computational weld mechanics to evaluate residual stresses and this paper describes the development of guidelines for using finite element analysis, which are now incorporated into the EDF Energy R6 defect assessment procedure, to determine stresses for use in the procedure. Prior to use in assessment the predicted results should be validated by comparison with measurements and the guidelines provide advice on the differing standards of validation which may be applied including the manufacture and testing of validation mock-ups.

This paper is part of a Themed Issue on Measurement, modelling and mitigation of residual stress.     

SectionBuilder: An innovative finite element tool for analysis and design of composite rotor blade cross-sections

SectionBuilder is a finite element based tool for analysis and design of composite rotor blade cross-sections. The tool can create the cross-sections with parametric shapes and arbitrary configurations. It has the ability to generate single- and multi-cell cross-sections with arbitrary lay-ups where the material properties for each layer can be defined on the basis of the design requirements. It can create the variation of thickness of skin and D-spars for rotor blades by considering ply drops. Cross-sections are often reinforced by core material for constructing realistic rotor blade cross-sections. The tool has the ability to integrate core materials into the cross-sections. After meshing the cross-section, the tool determines the sectional properties using finite element analysis. This tool computes sectional properties including stiffness matrix, compliance matrix, mass matrix, and principal axes. A visualization environment is integrated with the tool for visualizing the stress and strain distributions over the cross-section. The detail about the development steps and application of SectionBuilder is presented in this paper.     

基于Voxel有限元网格对球形夹杂复合材料的应力分析

通过Voxel有限元网格对球形夹杂复合材料进行应力分析时,由于Voxel网格在两相界面呈现阶梯状,所以在两相界面附近的单元会表现出明显的应力集中现象。提出采用局部应力平均方法来处理由于Voxel有限元网格而引起的应力集中,并且考虑应力平均区域、应力平均加权函数以及网格密度的影响。结果表明:该局部应力平均方法能够有效地去除两相界面附近单元的应力集中,但应力平均区域不能过大也不能过小。通过计算发现采用2个Voxel网格深度的平均区域为最优,并且具有网格不依赖性。该方法也可以进一步用于球形夹杂复合材料的积累损伤演化分析。     

Analysis of acoustic resonator with shape deformation using finite element method

An acoustic resonator with shape deformation has been analysed using the finite element method. The shape deformation is such that the volume of the resonator remains constant. The effect of deformation on the resonant frequencies is studied. Deformation splits the degenerate frequencies.