Discrete mesoscopic modeling for the simulation of woven-fabric reinforcement forming

A discrete modeling approach is proposed to simulate woven-fabric reinforcement forming via explicit finite element analysis. The tensile behaviour of the yarns is modeled by truss, beam or seatbelt elements, and the shearing behaviour of the fabric is incorporated within shell or membrane elements. This method is easy to set up using the user-defined material subroutine capabilities of explicit finite element programs. In addition, the determination of the material parameters is straightforward from conventional tensile and shear-frame tests. The proposed approach has been implemented in the ABAQUS and LS-DYNA explicit finite element programs. Two types of fabric, a plain-weave and a twill-weave Twintex® (commingled polypropylene and glass fibres) were characterized and used to validate the modeling approach. For this validation, shear-frame and bias-extension tests have been modeled, and the finite element results are compared to experimental data. The determination of experimental shear angle contours was possible via Digital Image Correlation (DIC). The finite element results from ABAQUS and LS-DYNA are similar and agree well with the experimental data. As an example of the capabilities of the method, the deep drawing of a hemisphere is simulated using both finite elements programs.     

Circuit theoretical approach to couple two-dimensional finiteelement models with external circuit equations

This paper presents a new method to couple two-dimensional finite element models with circuit equations. The method is based on handling of the finite element model as a circuit theoretical multiport element. This multiport element is treated in the same way as ordinary nonlinear circuit elements within the Newton-Raphson iteration of the circuit equations. The method has been utilized in a simulator program for analyzing power electronic drives in the time domain. The electrical machine is modeled by the two-dimensional finite element method. The power electronic circuit and the connections of the windings of the machine may have an arbitrary topology which is given by a net-list file (SPICE-type input file). The applicability of the method is investigated with two example cases which are verified by measurements. According to tests, the method proposed provides an effective and reliable way to construct simulators including finite element modeling     

双参数元的误差估计

双参数方法是构造高阶问题有限元(例如薄板弯曲问题单元)的有效方法。双参数元是一种非标准元,以往文献中只证明了它的收敛性。本文针对具体双参数板元给出它的误差估计式,并分析了节点参数的扰动量。     

Dynamic finite element formulation for Cosserat elastic plates

A displacement and rotation‐based dynamic finite element formulation for Cosserat plates is discussed in detail in this paper. Special attention is given to the validation of the element through adequate benchmarks and patch tests. The choice of the interpolation functions and the order of integration of the stiffness and the mass matrices are extensively argued. The possibility of local system deficiencies is explored, and a shear locking investigation specifically elaborated for Cosserat plates is carried out. It is shown how the present formulation has interesting computational properties as compared to a classical continuum‐based formulation and how it can provide suitable results despite the use of reduced integration. An example of application of the finite element is given, in which the natural frequencies of a masonry panel modelled by means of discrete elements are computed and compared with the finite elements solution. Copyright © 2014 John Wiley & Sons, Ltd.     

Shell topology optimization using the layered artificial material model

A general methodology for topology optimization using the finite element method is described for shell structures. Four‐ and nine‐node Reissner–Mindlin shell elements with drilling degrees of freedom are used for the finite element response analysis. The artificial material model is used in the topology optimization and in particular, an isotropic multi‐layer shell model is introduced to allow the formation of holes or stiffening zones. In addition, a single design variable resizing algorithm is implemented based on the existing criterion which is found to be adequate for the artificial material model. Several benchmark tests are presented to show the overall performance of the proposed methodology. The strain energy variation together with the variation of the layout of the structure is monitored. Some detailed examples are provided with comparisons of the use of the four‐ and nine‐node elements and studies of critical solution parameters. Copyright 2000 John Wiley & Sons, Ltd.     

Finite elements with embedded strong discontinuities for the modeling of failure in solids

This paper presents new finite elements that incorporate strong discontinuities with linear interpolations of the displacement jumps for the modeling of failure in solids. The cases of interest are characterized by a localized cohesive law along a propagating discontinuity (e.g. a crack), with this propagation occurring in a general finite element mesh without remeshing. Plane problems are considered in the infinitesimal deformation range. The new elements are constructed by enhancing the strains of existing finite elements (including general displacement based, mixed, assumed and enhanced strain elements) with a series of strain modes that depend on the proper enhanced parameters local to the element. These strain modes are designed by identifying the strain fields to be captured exactly, including the rigid body motions of the two parts of a splitting element for a fully softened discontinuity, and the relative stretching of these parts for a linear tangential sliding of the discontinuity. This procedure accounts for the discrete kinematics of the underlying finite element and assures the lack of stress locking in general quadrilateral elements for linearly separating discontinuities, that is, spurious transfers of stresses through the discontinuity are avoided. The equations for the enhanced parameters are constructed by imposing the local equilibrium between the stresses in the bulk of the element and the tractions driving the aforementioned cohesive law, with the proper equilibrium operators to account for the linear kinematics of the discontinuity. Given the locality of all these considerations, the enhanced parameters can be eliminated by their static condensation at the element level, resulting in an efficient implementation of the resulting methods and involving minor modifications of an existing finite element code. A series of numerical tests and more general representative numerical simulations are presented to illustrate the performance of the new elements. Copyright © 2007 John Wiley & Sons, Ltd.     

An improved EAS brick element for finite deformation

A new enhanced assumed strain brick element for finite deformations in finite elasticity and plasticity is presented. The element is based on an expansion of shape function derivatives using Taylor series and an extended set of orthogonality conditions that have to be satisfied for an hourglassing free EAS formulation. Such approach has not been applied so far in the context of large deformation three-dimensional problems. It leads to a surprisingly well-behaved locking and hourglassing free element formulation. Major advantage of the new element is its shear locking free performance in the limit of very thin elements, thus it is applicable to shell type problems. Crucial for the derivation of the residual and consistent tangent matrix of the element is the automation of the implementation by automatic code generation.     

A new eight-node quadrilateral shear-bending plate finite element

A new eight-node quadrilateral shear-bending Reissner–Mindlin plate finite element for the very thin and thick plates without locking and spurious zero-energy modes is presented. The element has very good convergence characteristics both for thin and thick plates, is hardly insensitive to mesh distortions, and passes the patch tests. The formulation of the element is derived from a displacement variational principle and some general criteria to compute inconsistent transverse shear strains. These criteria have been applied with success to four- and eight-node quadrilateral plate finite elements and could be applied to construct triangular elements. The eight-node quadrilateral shear-bending plate finite element proposed has been found to be very efficient.     

Implementation of an ANCF beam finite element for dynamic response optimization of elastic manipulators

Theoretical and practical aspects of an absolute nodal coordinate formulation (ANCF) beam finite element implementation are considered in the context of dynamic transient response optimization of elastic manipulators. The proposed implementation is based on the introduction of new nodal degrees of freedom, which is achieved by an adequate nonlinear mapping between the original and new degrees of freedom. This approach preserves the mechanical properties of the ANCF beam, but converts it into a conventional finite element so that its nodal degrees of freedom are initially always equal to zero and never depend explicitly on the design variables. Consequently, the sensitivity analysis formulas can be derived in the usual manner, except that the introduced nonlinear mapping has to be taken into account. Moreover, the adjusted element can also be incorporated into general finite element analysis and optimization software in the conventional way. The introduced design variables are related to the cross-section of the beam, to the shape of the (possibly) skeletal structure of the manipulator and to the drive functions. The layered cross-section approach and the design element technique are utilized to parameterize the shape of individual elements and the whole structure. A family of implicit time integration methods is adopted for the response and sensitivity analysis. Based on this assumption, the corresponding sensitivity formulas are derived. Two numerical examples illustrate the performance of the proposed element implementation.     

A generalized phase field multiscale finite element method for brittle fracture

A generalized multiscale finite element method is introduced to address the computationally taxing problem of elastic fracture across scales. Crack propagation is accounted for at the microscale utilizing phase field theory. Both the displacement-based equilibrium equations and phase field state equations at the microscale are mapped on a coarser scale. The latter is defined by a set of multinode coarse elements, where solution of the governing equations is performed. Mapping is achieved by employing a set of numerically derived multiscale shape functions. A set of representative benchmark tests is used to verify the proposed procedure and assess its performance in terms of accuracy and efficiency compared with the standard phase field finite element implementation.     

位移障碍下一个四阶变分不等式的双参数有限元逼近

研究位移障碍下的一个四阶变分不等式的非常规双参数有限元逼近。通过引入与常规单元不同的新技巧，得到了与常规有限元相同最优误差估计。这里的结论对几乎所有已知的非协调板元均适用。     

Finite elements based on energy orthogonal functions

It is shown how the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix. It is then attempted to construct a best possible stiffness matrix. The constraint equations restrict the way in which these stiffness terms may be chosen; however, there is normally still room for improving or optimizing an element. It is demonstrated how an element stiffness matrix may be found using rigid body, constant strain and higher order deformation modes. Further, it is shown how the constraint equations may be exploited in deriving an ‘energy orthogonality theorem’. This theorem opens the door to a whole new class of simple finite elements which automatically satisfy the convergence requirements. Examples of deriving plane stress and plate bending elements are given.     

The effects of element shape on the critical time step in explicit time integrators for elasto‐dynamics

In this paper, the effects of element shape on the critical time step are investigated. The common rule‐of‐thumb, used in practice, is that the critical time step is set by the shortest distance within an element divided by the dilatational (compressive) wave speed, with a modest safety factor. For regularly shaped elements, many analytical solutions for the critical time step are available, but this paper focusses on distorted element shapes. The main purpose is to verify whether element distortion adversely affects the critical time step or not. Two types of element distortion will be considered, namely aspect ratio distortion and angular distortion, and two particular elements will be studied: four‐noded bilinear quadrilaterals and three‐noded linear triangles. The maximum eigenfrequencies of the distorted elements are determined and compared to those of the corresponding undistorted elements. The critical time steps obtained from single element calculations are also compared to those from calculations based on finite element patches with multiple elements. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of microscopic damage events on static and ballistic impact strength of triaxial braid composites

The reliability of impact simulations for aircraft components made with triaxial braided carbon fiber composites is currently limited by inadequate material property data and lack of validated material models for analysis. Methods to characterize the material properties used in the analytical models from a systematically obtained set of test data are also lacking. A macroscopic finite element based analytical model to analyze the impact response of these materials has been developed. The stiffness and strength properties utilized in the material model are obtained from a set of quasi-static in-plane tension, compression and shear coupon level tests. Full-field optical strain measurement techniques are applied in the testing, and the results are used to help in characterizing the model. The unit cell of the braided composite is modeled as a series of shell elements, where each element is modeled as a laminated composite. The braided architecture can thus be approximated within the analytical model. The transient dynamic finite element code LS-DYNA is utilized to conduct the finite element simulations, and an internal LS-DYNA constitutive model is utilized in the analysis. Methods to obtain the stiffness and strength properties required by the constitutive model from the available test data are developed. Simulations of quasi-static coupon tests and impact tests of a represented braided composite are conducted. Overall, the developed method shows promise, but improvements that are needed in test and analysis methods for better predictive capability are examined.     

Polynomial approximation of shape function gradients from element geometries

A method is presented for the polynomial approximation of shape function gradients based solely on the geometry of finite element boundaries. The method is founded on a least squares approach which leads to an integration scheme satisfying a necessary condition for convergence. In its simplest form the method reduces to the well‐known uniform strain approach for finite elements. The method is applicable to a broad class of problems such as connecting dissimilar meshes, mesh adaptivity and transitioning, and the construction of finite elements with variable topologies. Finite elements based on the polynomial approximations are shown to pass patch tests of various orders. In contrast to standard elements, higher‐order patch tests are passed without the need for nodes internal to element boundaries. Less sensitivity to volumetric locking under plane strain conditions is demonstrated through comparisons with a standard element formulation. Copyright © 2001 John Wiley & Sons, Ltd.     

Hierarchal triangular elements using orthogonal polynomials

Hierarchal elements are finite elements which have the useful property that elements with different polynomial orders can be used together in the same mesh without causing discontinuities. This paper introduces a new hierarchal triangular element in which the basis functions are constructed from orthogonal polynomials—Jacobi polynomials. The resulting element is shown to be better conditioned than the earlier hierarchal element of Rossow and Katz.¹ Recursive formulas allow the complete set of basis functions for an element to be efficiently evaluated at a given point. In addition, the formulas can be used to generate pre-computed (universal) matrices. Examples are given of universal matrices, up to order 4, for the generalized Helmholtz equation. An electromagnetic problem involving a length of transmission line is used to show the usefulness of the new elements.     

一种新型的时域动力无穷单元

针对频域动力无穷元不便与时域有限元结合的缺陷,采用时域的波传函数,推导出一种新型的时域动力无穷单元,并采用UPFs工具对ANSYS进行二次开发,将其嵌入到ANSYS当中。然后采用经典算例对所提出的新型动力无穷单元进行验证,并将其结果与远置边界、粘性边界、粘弹性边界的结果进行比较。验证结果表明,所提出的新型时域动力无穷单元是成功的,并可方便地实现与时域的有限单元结合。     

Free mesh method: A new meshless finite element method

A new meshless finite element method, named as the Free Mesh Method, is proposed in this paper. Once nodes are arranged in the domain to be analyzed, some temporary triangular elements are set around a node, i.e. a current central node. The contributions from the element matrices of the above temporary elements are assemebled to the total stiffness matrix. The above processes are performed on all the nodes in the domain. Finally, the solution is obtained by solving the total stiffness equation system as the usual finite element method. To demonstrate the effectiveness of the method, a simple two-dimensional heat conduction problem is solved.     

假设位移拟协调平面单元应变离散算法研究

应变-位移方程的弱化和离散是拟协调有限元列式中的一个基本问题,也是假设应变有限元方法的一个重要问题。该文通过研究拟协调有限元中的平面单元列式,考察了不同应变离散算法下单元的性能。通过理论分析和数值实验,证明了对同一个应变项的计算可以选择不同的应变-位移式进行计算,应变-位移式的选择并不影响所构造单元的收敛性。该文结果解决了拟协调有限元的一个基础问题,可以指导拟协调有限元的列式,也为一般的弹性力学数值分析中应变-位移方程的处理提供依据。     

Recovery of equilibrium on star patches from conforming finite elements with a linear basis

A previous technique for recovering equilibrated stresses from compatible finite element models of structural mechanics problems is extended to cover those cases where the partitioned loads applied to star patches are not initially balanced, regarding rotational equilibrium. The residual moments are removed by adding a suitable corrective stress field to the compatible one before deriving the fictitious body forces. Corrective stress fields are determined by solving another set of local problems based on subdomains that each contain elements forming a neighbourhood of a loaded kernel element. The conditions for the existence of a solution of these problems are studied for simplicial elements. The parameters that control the extended technique are assessed from numerical tests on a variety of two‐dimensional linear elastic problems based on constant strain elements for the compatible solutions. These tests are presented in the context of computing bounds on quantities of interest such as total strain energy and local reactions and displacements. Copyright © 2011 John Wiley & Sons, Ltd.