THE EFFECT OF INITIAL DISPLACEMENTS ON PROBLEMS OF LARGE DEFLECTION AND STABILITY
Abstract
A finite element approach is used to obtain equations for large displacement and stability analysis via the principle of virtual work. The equations are then written in incremental form. It is found that the inclusion of the nonlinear strain displacement terms results in two additional 'initial stiffness' matrices. The first is the well known 'initial stress' matrix. An alternate general method is proposed for the derivation of the 'initial stress' matrix. The second matrix is a function of previous displacements and is referred to here as the 'initial displacement' matrix. It is obtained as a result of writing the nonlinear strain displacement relations in incremental form. The 'initial displacement' matrix was found to be of the same order as the 'initial stress' matrix but appears not to have been previously recognized in finite element analysis. Results obtained for a simple truss and an arch problem agreed with results in the literature. Analysis without the 'initial displacement' matrix resulted in an overestimate of the buckling loads by factors of 1.8 and 2 for the truss and arch respectively. A linear eigenvalue analysis resulted in an overestimate of the buckling load by factors of 5 and 2 respectively.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1967
- Accession Number
- AD0664979
Entities
People
- P. V. Marcal
Organizations
- Brown University