On the extremum complementary energy principles for nonlinear elastic shells

1990 ◽  
Vol 26 (5-6) ◽  
pp. 683-693 ◽  
Author(s):  
Gao Yang ◽  
Y.K. Cheung
Keyword(s):  
Complementary Energy ◽  
Elastic Shells ◽  
Nonlinear Elastic ◽  
Energy Principles

Finite Elasticity Solutions Using Hybrid Finite Elements Based on a Complementary Energy Principle—Part 2: Incompressible Materials

1979 ◽  
Vol 46 (1) ◽  
pp. 71-77 ◽  
Author(s):  
H. Murakawa ◽  
S. N. Atluri
Keyword(s):  
Finite Elasticity ◽  
Strain Analysis ◽  
Companion Paper ◽  
Complementary Energy ◽  
Energy Principle ◽  
Complementary Energy Principle ◽  
Elasticity Solutions ◽  
Strip Test ◽  
Nonlinear Elastic ◽  
Incompressible Rubber

In a companion paper [1], the authors presented a total Lagrangean rate formulation for a hybrid stress finite-element method, based on a rate complementary energy principle which involves both the rates of Piola-Lagrange stress and rotation as variables, for finite strain analysis of nonlinear elastic compressible solids. In this paper the method is extended to the case of precisely incompressible rubber-like materials. Two plane stress problems, one corresponding to a biaxial strip test and, the other, a sheet with a circular hole, both involving strains in excess of 100 percent, are solved and the numerical results are discussed.

Finite Elasticity Solutions Using Hybrid Finite Elements Based on a Complementary Energy Principle

1978 ◽  
Vol 45 (3) ◽  
pp. 539-547 ◽  
Author(s):  
H. Murakawa ◽  
S. N. Atluri
Keyword(s):  
Finite Elasticity ◽  
Strain Analysis ◽  
Elastic Solid ◽  
Element Model ◽  
Equilibrium Equations ◽  
Complementary Energy ◽  
Rotation Tensor ◽  
Energy Principle ◽  
Complementary Energy Principle ◽  
Nonlinear Elastic

The possibility of deriving a complementary energy principle, for the incremental analysis of finite deformations of nonlinear-elastic solids, in terms of incremental Piola-Lagrange (unsymmetric) stress alone, is examined. A new incremental hybrid stress finite-element model, based on an incremental complementary energy principle involving both the incremental Piola-Lagrange stress, and an incremental rotation tensor which leads to discretization of rotational equilibrium equations, is presented. An application of this new method to the finite strain analysis of a compressible nonlinear-elastic solid is included, and the numerical results are discussed.

Homogenization and Global Responses of Inhomogeneous Spherical Nonlinear Elastic Shells

2006 ◽  
Vol 82 (3) ◽  
pp. 193-214 ◽  
Author(s):  
Yi-Chao Chen ◽  
K. R. Rajagopal ◽  
Lewis Wheeler
Keyword(s):  
Elastic Shells ◽  
Nonlinear Elastic

Complementary energy principles in dissipative fluids

1982 ◽  
Vol 23 (3) ◽  
pp. 460-463 ◽  
Author(s):  
E. W. Laedke ◽  
K. H. Spatschek
Keyword(s):  
Complementary Energy ◽  
Energy Principles ◽  
Dissipative Fluids
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