Efficient finite element analysis using graph-theoretical force method; rectangular plane stress and plane strain Lagrange family elements

A generalization of the stability analysis is presented: analogously to the stability analysis of equilibrium, based on the potential energy, stability analysis of compatibility, based on the complementary energy will be introduced. 
Nonlinearly inelastic material is considered, excluding strain softening and damage but including strain hardening and locking. The concept of tangent and compliance modulus is applied. 
Global stability analysis is investigated, related to the total domain of the state variables,distinguishing the dead and rigid type of load, and their relation with the basic variational principles. 
Discrete structural model of frame structures with uniaxial nonlinear and nonelastic material behaviour will be analysed. 
Numerical illustrations can be studied in the author's papers, in (KURUTZ 1989, 1993, 1994).

Stability of equilibrium and compatibility of structures with uniaxial material behaviour

Systematization of complex nonlinearities, the wide-ranging linearization concepts are
detailed in [3], [4] related to material, strain, displacement and loading type
nonlinearities and their interaction. In this paper, an illustration of the full geometric
nonlinearity, the interaction of the strain and displacement nonlinearities are presented, by
means of the finite element model of the Timoshenko beam.

Marta Kurutz

Papers

Stability of equilibrium and compatibility of structures with uniaxial material behaviour

Illustration of the Interaction of Strain and Displacement Nonlinearities in the Structural Tangent Stiffness