Nonlinear Finite Elements for Continua and Structures Part 5 pptx

... 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...

Ngày tải lên: 12/08/2014, 02:20

... ) I * =1 2n N ∑ (9.3.2b) 9-9 66 1 .51 .00 .50 .0-0 .5 -4 -3 -2 -1 0 1 Log (H) Log (displacement norm) 1 .51 .00 .50 .0-0 .5 -0 .5 0.0 0 .5 1.0 1 .5 2.0 Log (H) Log (energy norm) QUAD4 ASOI and OI ADS ASMD QBI, ASQBI, and Pian-Sumihara Figure ... (2x2) 6.98 (1.79) 7 .52 (3.62) 7.86 (4 .53 ) 8. 05 (4.99) 7.27 (3.10) 7.68 (4.17) ASQBI (2 pt) 7.00 (1. 75) 7 .53 (3 .54 ) 7.87 (4 .57...

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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 ... kinematic Voigt rule, see Appendix B and Eqs.(4 .5. 18) and (4 .5. 19) hold as before. The conversion of the internal nodal force expression to the Voigt form (4 .5....

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... are static and do not include acceleration. The momentum and equilibrium equations are tensor equations, and the tensor forms (3 .5. 33) and (3 .5. 37) represent n SD scalar equations. 3 .5. 8 Reynold's ... loads are applied slowly and the inertial forces are very small and can be neglected. In that case, the acceleration in the momentum equation (3 .5. 35) can be dropped a...

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... equations for the updated Lagrangian formulation, as given in Box 5. 5. The nodal forces in the updated and total Lagrangian formulations are expressed in terms of different variables and integrated ... (E4 .5. 2) where T is given by (E4 .5. 1). As can be seen from the above, the master nodal forces are the sum of the master nodal forces for the disjoint model and the transforme...

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... = C 11 C 12 C 13 C 14 C 15 C 16 C 22 C 23 C 24 C 25 C 26 C 33 C 34 C 35 C 36 C 44 C 45 C 46 sym C 55 C 56 C 66                   ε 1 ε 2 ε 3 ε 4 ε 5 ε 6     ... µ 0 δ ik δ jl +δ il δ kj ( ) (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 \par...

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... 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, and hence ... difference formulas for the velocity and acceleration. We consider here its application to Lagrangian meshes with rate- independent materials. Geometric and material nonlinearites are i...

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... stable time step. For the trapezoidal rule, α = 0 .5 , and for any 0 .5 < α ≤ 1 the method is unconditionally stable. For 0 ≤α < 0 .5 , the integrator is implicit but conditionally stable, ... 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 c...

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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 ... elements. Mesh generators for quadrilateral elements tend to be less robust and more time consuming. Therefore, triangular and tetrahedral elements are preferable when...

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... Carpenter and J.S J. Ong, "Stress projection for membrane and shear locking in shell finite elements, " Comput. Methods Appl. Mech. Engrg., 51 , 221- 258 (19 85) . T. Belytschko and C.S. ... "Analysis of Thick and Thin Shell Structures by Curved Finite Elements, " IJNME, VOL2, 419- 451 . T. Belytschko, B.L. Wong and H Y. Chiang "Advances in one-po...

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