Asymmetric Spatial Beams with Symmetric Kinetostatic Behaviour

Abstract

A method to achieve symmetric kinetostatic behaviour in an extensive working range at the endpoint of an asymmetric spatial beam, using cross-section optimization, is presented. The objective function of the optimization is defined as expanding the beam working range to the desired region, simultaneously maximizing symmetric behaviour in it. To reach this goal, a beam with predefined spatial global shape and an ‘I’ cross-section selected. The cross-sectional dimensions throughout the beam are used as input values for the optimization. The endpoint displacements under symmetric loadings are attained using a nonlinear co-rotational beam element based on the Euler-Bernoulli beam formulation. The optimized beams are compared to a circular cross-section beam with the same global shape to show the efficacy of the method. Isoforce diagrams are investigated for the optimized beams to show the symmetry behaviour of the beam endpoint and the effect of changing different parameters in cross-sectional optimization is discussed.