Wavelet basis finite element solution of structural dynamics problems

Purpose - The purpose of this paper is to present a new hierarchical finite element formulation for approximation in time. Design/methodology/approach - The present approach using wavelets as basis functions provides a global control over the solution error as the equation of motion is satisfied for the entire duration in the weighted integral sense. This approach reduces the semi-discrete system of equations in time to be solved to a single algebraic problem, in contrast to step-by-step time integration methods, where a sequence of algebraic problems are to be solved to compute the solution. Findings - The proposed formulation has been validated for both inertial and wave propagation types of problems. The stability and accuracy characteristics of the proposed formulation has been examined and is found to be energy conserving. Originality/value - The paper presents a new hierarchical finite element formulation for the solution of structural dynamics problems. This formulation uses wavelets as the analyzing basis for the desired transient solution. It is found to be very well behaved in solution of wave-propagation problems.