NEHRP Clearinghouse

Solution Techniques for Linear and Nonlinear Dynamics of Structures Modeled by Finite Elements.
Adeli, H.
National Science Foundation, Washington, DC. Engineering and Applied Science., June 1976, 209 p.
Identifying Number(s)
Competitive solution techniques for linear and nonlinear dynamic analysis of structures by the finite element method are described. The accuracy, stability, and efficiency of the solution procedures are examined by comparing the results from a plane stress sample problem. An efficient operational procedure is developed for the isoparametric quadrilateral, the type of element used, in order to avoid matrix multiplications. The use of a lumped mass approach, resulting in a diagonal mass matrix, is shown to be more efficient than the non-diagonal mass formulation because the equations of motion are uncoupled in the acceleration terms. A comparison of four solution techniques indicates that direct linear extrapolation with trapezoidal rule is the best technique for linear dynamic analysis. For nonlinear analysis, both material and geometric nonlinearities are included in the finite element formation. An investigation involving three implicit and three explicit methods is evaluated and recommendations are made. Algorithms for these solution techniques are developed and are implemented in three computer programs. The appendices contain an operational procedure for calculating the stiffnesses and equivalent nodal loads and a lumped mass matrix for an isoparametric quadrilateral.
Structures; Stress strain diagrams; Stiffness methods; Explicit methods; Matrix methods; Finite element analysis; Earthquake engineering; Implicit methods; Computer programming; Linear systems; Nonlinear systems; Earthquakes; Dynamic structural analysis