Nonlinear Finite Elements for Continua and Structures Part 10 ppt

... configuration and the motion from a reference configuration is often not known explicitly. In Eulerian finite elements, the elements are fixed in space and material convects through the elements. ... Eulerian elements may also lack resolution in the most highly deforming regions of the body. The aim of ALE finite element formulations is to capture the advantages of both Lagrangi...

Ngày tải lên: 12/08/2014, 02:20

... Mechanics, December 16, 1998 30 For the subsequent stages of deformation, we only give the motion, the deformation gradient, its inverse and rate and the rate-of-deformation and Green strain tensors. configuration ... Cauchy stress and corotational rate-of- deformation. Its equivalence to the power in terms of the unrotated Cauchy stress and rate-of-deformation is easily demonstra...

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... polynomials for rectangular elements and is smooth and nearly a polynomial for isoparametric elements. In nonlinear analysis, the integrand is not always smooth. For example, for an elastic-plastic ... weak form and showed that it implies the strong form. This, combined with the development of the weak form from the strong form, shows that the weak and strong forms are eq...

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... Shells and Structures, December 16, 1998 CHAPTER 9 SHELLS AND STRUCTURES DRAFT by Ted Belytschko Northwestern University Copyright 1997 9.1 INTRODUCTION Shell elements and other structural elements ... motion in the weak form of the momentum equations for continua or 2. imposed directly on the discrete equations for continua. Thus the CB shell formulation is a more strai...

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... challenges and opportunities in nonlinear finite element analysis. 1.2. RELATED BOOKS AND HISTORY OF NONLINEAR FINITE ELEMENTS Several excellent texts and monographs devoted either entirely or partially to ... usefulness and potential of nonlinear finite element analyses are very sanguine. In many industries, nonlinear finite element analysis have shortened design cy...

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... master nodal forces are the sum of the master nodal forces for the disjoint model and the transformed slave node forces. These formulas apply to both the external and internal nodal forces. The ... Lagrangian formulation and the total Lagrangian formulation are identical. The numerical values for the nodal forces obtained by either formulation are also identical. Each of these formu...

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... rate-independent and incrementally linear and reversible. This means that for small increments about a finitely deformed state, the increments in stress and strain are linearly related and are recovered ... ) (5.4.40) and where λ 0 and µ 0 are Lamé constants. Noting that µ 0 and that \begin{equation} {\bf S} = 2{\partial \Psi({\bf C})\over \partial {\bf C}} = {\partial W({\b...

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... difference formulas for the velocity and acceleration. We consider here its application to Lagrangian meshes with rate- independent materials. Geometric and material nonlinearites are included, and ... with deformation. In the updated Lagrangian form, (4.5.5) the domain of the element (or body), the spatial derivatives ∂N I / ∂x j and the Cauchy stress depend on the deformation,...

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... Petrov-Galerkin finite elements for nonlinear continua , Comput. Meths. Appl. Mech. Engrg., 68, 259- 310. Benson, D.J.,(1989), ‘An efficient, accurate simple ALE method for nonlinear finite element ... ???. The next highest order elements are the 6-node triangle and the 8 and 9 node quadrilaterals. The counterparts in three dimensions are the 10 node tetrahedron and...

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... tensor and the PK2 stress when it is advantageous for a particular constitutive law. Moreover any updated Lagrangian formulation can easily be changed to a Lagrangian formulation by a transformation ... element in their attractiveness is that it eliminates for reformulating the many ingredients of continuous finite elements for shells. The Hu-Washizu weak form is then given by δ...

Ngày tải lên: 12/08/2014, 02:20