The higher order simulations are compared to traditional linear basis finite element methods. Each methods cost in attaining a fixed level of accuracy is assessed and cubic hexahedral elements are seen to be the most efficient. This paper presents an analytical fully recursive design sensitivity algorithm, a direct differentiation approach, to facilitate first-order sensitivity analysis in optimal design problems of multibody dynamic systems. Advancement of the algorithm permits processing the calculation of sensitivity matrix in parallel with the procedures for state equations formulation. The algorithm presented avoids the massive numbers of operations involved in explicitly generating and solving sensitivity equations for systems involving a combination of many state variables and design parameters.
Current development focuses on chain systems to illustrate the recursive nature of the algorithm.
Extension of the procedure to the classes of arbitrary tree topologies is straightforward. Solution accuracy of the algorithm is demonstrated by a numerical example of planar double pendulum. The fitness difference between two strings is usually neglected in most crossover operators. The neglect of this useful information often results in the less efficient propagation of search trials into fitness improved regions, and a general increase in the number of function evaluations required to obtain a converged solution. An alternative crossover strategy is presented which brings this information into consideration to assist locating search trials.