On accurate descriptions for primary and secondary paths in equilibrium problems

• Published in: Computers & structures Vol. 44; no. 1; pp. 229 - 242
• Main Author: Eriksson, A.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Oxford Elsevier Ltd 1992; Elsevier Science
• Subjects: Algorithms; Bifurcation behaviour; Buckling; Computer programming; Elastic stability theory; Equilibrium problems; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Mathematical models; Numerical methods; Physics; Solid mechanics; Structural analysis; Structural and continuum mechanics; Displacement(deformation); Elastic stability; Non linear effect; Equilibrium equation; Boundary element method; Structural analysis
• ISSN: 0045-7949; 1879-2243; 1879-2243
• DOI: 10.1016/0045-7949(92)90242-R

The paper describes how several procedures, based on ideas and expressions from the analytical elastic stability theory, have been introduced as numerical tools in a general finite element program for geometrically non-linear structural analysis. Derivatives of the tangential stiffness matrix are utilized for improved predictions in the step-wise solution of equilibrium states, for identification of critical points and for accurate descriptions of initial post-bifurcation behaviour. The methods are used in a general solution algorithm, based on a parameterizing component formulation. For some element types, analytical expressions for these derivatives can be developed. The corresponding numerical approximations, needed in other element types, are also discussed. Other practical details in the numerical implementation are given. Two numerical frame examples, showing different types of limit and bifurcation behaviours, are used to discuss the numerical properties of the methods.