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1.
A formulation for frictionless contact problems using a weak form introduced by Nitsche 总被引:1,自引:1,他引:0
In this paper a finite element formulation for frictionless contact problems with non-matching meshes in the contact interface
is presented. It is based on a non-standard variational formulation due to Nitsche and leads to a matrix formulation in the
primary variables. The method modifies the unconstrained functional by adding extra terms and a stabilization which is related
to the classical penalty method. These new terms are characterized by the presence of contact forces that are computed from
the stresses in the continuum elements. They can be seen as a sort of Lagrangian-type contributions. Due to the computation
of the contact forces from the continuum elements, some additional degrees-of-freedom are involved in the stiffness matrix
parts related to contact. These degrees-of-freedom are associated with nodes not belonging to the contact surfaces. 相似文献
2.
Geir Horrigmoe 《International journal for numerical methods in engineering》1978,12(12):1819-1839
The present paper describes a hybrid stress finite element formulation for geometrically non-linear analysis of thin shell structures. The element properties are derived from an incremental form of Hellinger-Reissner's variational principle in which all quantities are referred to the current configuration of the shell. From this multi-field variational principle, a hybrid stress finite element model is derived using standard matrix notation. Very simple flat triangular and quadrilateral elements are employed in the present study. The resulting non-linear equations are solved by applying the load in finite increments and restoring equilibrium by Newton-Raphson iteratioin. Numerical examples presented in the paper include complete snap-through buckling of cylindrical and spherical shells. It turns out that the present procedure is computationally efficient and accurate for non-linear shell problems of high complexity. 相似文献
3.
Howard L. Schreyer Joseph J. Fedock 《International journal for numerical methods in engineering》1979,14(9):1379-1398
Orthogonal base functions that are complete first-order polynomials but contain higher order terms are developed for normalized rectangular and triangular elements. To obtain exact expressions for kinetic energy under rigid body rotation, an internal node is introduced at the centroid of each element. Then the corresponding mass matrix is both diagonal and consistent. A mixed variational formulation is used in the derivation of spatially discretized field equations. Central Difference time integration is utilized to provide sample results which are compared with other numerical or analytical solutions. 相似文献
4.
流体固体动力耦合分析的有限元法 总被引:10,自引:2,他引:8
应用有限元法探讨了流体、固体接触界面由无限接触点对组成,并以接触点对的瞬态接触内力作为待定变量的流体固体动力耦合模型的数值求解方法.分析了流体、固体域插值函数的特点,用二维八节点等参元及流固接触面上的接触点对单元,对流固耦合系统进行了离散化处理;并采用变分原理推导了反映流体固体动力相互作用机理的接触约束矩阵(或称动力耦合矩阵),建立了有限元控制方程,给出了完整的数值计算方法, 研编了动力耦合系统的分析程序.数值计算结果与经典理论解误差很小,验证了动力耦合模型和有限元求解方法的正确性及其较高的计算精度. 相似文献
5.
In this paper, six-node hybrid-Trefftz triangular finite element models which can readily be incorporated into the standard
finite element program framework in the form of additional element subroutines are devised via a hybrid variational principle
for Helmholtz problem. In these elements, domain and boundary variables are independently assumed. The former is truncated
from the Trefftz solution sets and the latter is obtained by the standard polynomial-based nodal interpolation. The equality
of the two variables are enforced along the element boundary. Both the plane-wave solutions and Bessel solutions are employed
to construct the domain variable. For full rankness of the element matrix, a minimal of six domain modes are required. By
using local coordinates and directions, rank sufficient and invariant elements with six plane-wave modes, six Bessel solution
modes and seven Bessel solution modes are devised. Numerical studies indicate that the hybrid-Trefftz elements are typically
50% less erroneous than their continuous Galerkin element counterpart. 相似文献
6.
Based upon a variational principle and the associated theory derived in three preceding papers, an expression for the magneto-elastic buckling value for a system of an arbitrary number of parallel superconducting beams is given. The total current is supposed to be equal both in magnitude and direction for all beams, and the cross-sections are circular. The expression for the buckling value is formulated more explicitly in terms of the so-called buckling amplitudes, the latter following from an algebraic eigenvalue problem. The pertinent matrix is formulated in terms of complex functions, which are replaced by real potentials. The matrix elements are calculated by a numerical method, solving a set of intergral equations with regular kernels. Apart from the buckling value(s) the buckling modes are also obtained. Finally, our results are compared with the results of a mathematically less complicated theory, i.e. the method of Biot and Savart. 相似文献
7.
M. C. Bouzeghoub M. J. Gunn 《International journal for numerical methods in engineering》1994,37(6):895-904
A technique is proposed for the selection of stress interpolations for hybrid models. The present paper applies this approach to plane problems. The stiffness matrix is derived using the Hellinger–Reissner variational principle. This formulation uses infinitesimal equilibrium relationships and divides the assumed stress into its lower-order and higher-order parts. The patch test can be passed and the resulting elements are generally invariant. A plane four-node quadrilateral element is described and compared with existing elements. Numerical studies show that the accuracy of the element is generally good. 相似文献
8.
A simple procedure to formulate efficient and stable hybrid/mixed finite elements is developed, for applications in macro- as well as micromechanics. In this method, the strain and displacement field are independently assumed. Instead of using two-field variational principles to enforce both equilibrium and compatibility conditions in a variational sense, the independently assumed element strains are related to the strains derived from the independently assumed element displacements, at a finite number of collocation points within the element. The element stiffness matrix is therefore derived, by simply using the principle of minimum potential energy. Taking the four-node plane isoparametric element as an example, different hybrid/mixed elements are derived, by adopting different element strain field assumptions, and using different collocation points. These elements are guaranteed to be stable. Moreover, the computational efficiency of these elements is far better than that for traditional hybrid/mixed elements, or even better than primal finite elements, because the strain field is expressed analytically as simple polynomials (whereas, in isoparametric displacement-based element, the strain field is far more complicated), with nodal displacements as unknowns. The essential idea is thereafter extended to Voronoi cell finite elements, for micromechanical analysis of materials. Neither these four-node hybrid/mixed elements nor the Vonroni cell finite elements need to satisfy the equilibrium conditions a priori, making them suitable for extension to geometrically nonlinear and dynamical analyses. Various numerical experiments are conducted using these new elements, and the results are compared to those obtained by using traditional hybrid/mixed elements and primal finite elements. Performances of the different elements are compared in terms of efficiency, stability, invariance, locking, sensitivity to mesh distortion, and convergence rates. 相似文献
9.
10.
11.
The Boundary Contour Method (BCM) is a recent variant of the Boundary Element Method (BEM) resting on the use of boundary
approximations which a-priori satisfy the field equations. For two-dimensional problems, the evaluation of all the line-integrals
involved in the collocation BCM reduces to function evaluations at the end-points of each element, thus completely avoiding
numerical integrations.
With reference to 2-D linear elasticity, this paper develops a variational version of BCM by transferring to the BCM context
the ingredients which characterize the Galerkin-Symmetric BEM (GSBEM). The method proposed herein requires no numerical integrations:
all the needed double line-integrals over boundary elements pairs can be evaluated by generating appropriate “potential functions”
(in closed form) and computing their values at the element end-points. This holds for straight as well as curved elements;
however the coefficient matrix of the equation system in the boundary unknowns turns out to be fully symmetric only when all
the elements are straight. The numerical results obtained for some benchmark problems, for which analytical solutions are
available, validate the proposed formulation and the corresponding solution procedure. 相似文献
12.
13.
P. Bettess O. C. Zienkiewicz 《International journal for numerical methods in engineering》1977,11(8):1271-1290
The wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined. Appropriate boundary conditions are described, for finite and infinite boundaries. These equations are then presented in a variational form, which is used as a basis for finite and infinite elements. The elements are used to solve a wide range of unbounded surface wave problems. Comparisons are given with other methods. It is concluded that infinite elements are a competitive method for the solution of such problems. 相似文献
14.
Zhong Wanxie Lin Jiahao Qiu Chunhang 《International journal for numerical methods in engineering》1992,33(1):197-211
The theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues. From the minimum potential energy variational principle of the substructural chain, the generalized variational principle with two kinds of variables is derived first. By comparing that generalized variational principle with the variational principle in LQ control theory, the simulation relation is established. Based on that relation, the potential energy and mixed energy formulation of the algebraic Riccati equations are derived, then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix. By using the solutions of the positive and negative co-ordinate algebraic Riccati equations, the canonical transformation matrices for the eigenproblems of the substructural chain and LQ control are constructed respectively, which reduce the eigenproblem to half-size. The properties of the solutions are analysed, which establishes the basis for expansion solutions. 相似文献
15.
By interacting and synchronizing wavelet theory in mathematics and variational principle in finite element method, a class
of wavelet-based plate element is constructed. In the construction of wavelet-based plate element, the element displacement
field represented by the coefficients of wavelet expansions in wavelet space is transformed into the physical degree of freedoms
in finite element space via the corresponding two-dimensional C1 type transformation matrix. Then, based on the associated generalized function of potential energy of thin plate bending
and vibration problems, the scaling functions of B-spline wavelet on the interval (BSWI) at different scale are employed directly
to form the multi-scale finite element approximation basis so as to construct BSWI plate element via variational principle.
BSWI plate element combines the accuracy of B-spline functions approximation and various wavelet-based elements for structural
analysis. Some static and dynamic numerical examples are studied to demonstrate the performances of the present element. 相似文献
16.
J. Zhang N. Katsube 《International journal for numerical methods in engineering》1995,38(10):1635-1653
A hybrid finite element approach is proposed for the mechanical response of two-dimensional heterogeneous materials with linearly elastic matrix and randomly dispersed rigid circular inclusions of arbitrary sizes. In conventional finite element methods, many elements must be used to represent one inclusion. In this work, each inclusion is embedded inside a polygonal element and only one element is required to represent one inclusion. In numerically approximating stress and displacement distributions around the inclusion, classical elasticity solutions for a multiply-connected region are employed. A modified hybrid functional is used as the basis of the element formulation where the displacement boundary conditions of the element are automatically considered in a variational sense. The accuracy and efficiency of the proposed method are demonstrated by two boundary value problems. In one example, the results based on the proposed method with only 64 hybrid elements (450 degrees of freedom) are shown to be almost identical to those based on the traditional method with 2928 conventional elements (5526 degrees of freedom). 相似文献
17.
The variational formulation of a problem is frequently used in strength analysis of parts and structural elements. The authors present a variational principle whose Euler's equations are the differential equations of thermoelasticity for stresses. 相似文献
18.
The paper is concerned with variational sensitivity analysis of a nonlinear solid shell element, which is based on the Hu–Washizu variational principle. The sensitivity information is derived on the continuous level and discretized to yield the analytical expressions on the computational level. Especially, the pseudo load matrix and the sensitivity matrix, which dominate design sensitivity analysis of shape optimization problems, are derived. Because of the mixed formulation, condensation of the pseudo load matrix on the element level is performed to compute the sensitivity matrix. An illustrative example from the field of geometry‐based shape optimization demonstrates the possible application of the presented formulation. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
Rezak Ayad Gouri Dhatt Jean Louis Batoz 《International journal for numerical methods in engineering》1998,42(7):1149-1179
A valuable variational approach for plate problems based on the Reissner–Mindlin theory is presented. The new MiSP (Mixed Shear Projected) approach is based on the Hellinger–Reissner variational principle, with a particular representation of transversal shear forces and transversal shear strains. The approximations of the shear forces are derived from those of the bending moments using the corresponding equilibrium relations. The shear strains are defined in terms of the edge tangential strains that are projected on the element degrees of freedom. Two finite elements are developed on the MiSP approach basis: 3-node triangular element MiSP3 and 4-node quadrilateral element MiSP4. Both elements can be considered as the most simple among the existent mixed elements. A modified MiSP model with a derived 4-node element is also presented. Numerical experiments are presented which show that the MiSP elements do not exhibit shear locking and give excellent results for thick and thin plates. They also pass the patch test for a general triangle and quadrilateral. © 1998 John Wiley & Sons, Ltd. 相似文献
20.
基于区间B样条小波(B-Spline Wavelet on the Interval, BSWI)和多变量广义势能函数,该文构造了二类变量小波有限单元,并用于一维结构的弯曲与振动分析。基于广义变分原理,从多变量广义势能函数出发,推导得到多变量有限元列式,并以区间B样条小波尺度函数作为插值函数对两类广义场变量进行离散。此单元的优势在于可以提高广义力的求解精度,因为在传统有限元中,只有一类广义位移场函数,所以广义力通常是通过对位移的求导得到,而多变量单元中,广义位移和广义力都是作为独立变量处理的,避免了求导运算。此外,区间B样条小波是现有小波中数值逼近性能非常好的小波函数,以它作为插值函数可进一步保证求解精度。转换矩阵的应用,可以将无任何明确物理意义的小波系数转换到相应的物理空间,方便了问题的处理。最后,通过数值算例对Euler梁和平面刚架的分析,验证了此单元的正确性和有效性。 相似文献