Generalized finite strains, generalized stresses, and a principle of virtual work for finite-element computer programs

Technical Report · Mon Aug 01 04:00:00 EDT 1988

OSTI ID:6685663

Cook, W A; Genin, J

This report compares strain and stress tensors and virtual work principles of the Lagrangian and Eulerian formulations. A generalized formulation is presented that includes the Lagrangian and Eulerian formulations as special cases. This formulation uses a reference configuration that is a linear combination of the deformed and undeformed configurations. Generalized strain and stress tensors are presented that include, as special cases, Green strain and Piola--Kirchhoff stress tensors of the Lagrangian formulation and Almansi strain and Cauchy stress tensors of the Eulerian formulation. Similarly, a generalized virtual work principle is presented that includes, also as special cases, the principles of virtual work for the Lagrangian and Eulerian formulations. Two approaches are presented for solving nonlinear stress analysis problems with the generalized formulation. Both use the finite-element method to approximate equilibrium: one iterates the nodal displacements, and the other iterates the incremental displacements. 3 refs.

• Research Organization: Los Alamos National Lab., NM (USA)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6685663
• Report Number(s): LA-11371-MS; ON: DE89002102
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990230* -- Mathematics & Mathematical Models-- (1987-1989)
BOUNDARY CONDITIONS
FINITE ELEMENT METHOD
FUNCTIONS
ITERATIVE METHODS
LAGRANGIAN FUNCTION
NUMERICAL SOLUTION
STRAINS
STRESS ANALYSIS
TENSOR FORCES