A nonlinear finite element approach to kineto-static analysis of elastic beams

Abstract

Recently the demand for higher speed in design of mechanical systems has led to an intensive research in the formulation of the elastic mechanisms. In this study it is shown that the kineto-static solution is close to full dynamic solution for typical dimensions of the links. The formulation presented here uses the Timoshenko Beam Model with geometric stiffening. The element matrices and nodal forces are reported as integral of product of shape functions. This gives a more generic form and can be easily applied to other shape functions. A new formalism is introduced for the nonlinear effect (geometric stiffening). Fundamental to this approach is the introduction of a tensor and its assembly which plays a similar role as element matrices of the linear terms. Several numerical simulations are conducted to quantify the effect of geometric stiffening, tip mass, and normal and tangential acceleration on the nodal displacements.