The beam elements, which are widely used in the absolute nodal coordinate formulation (ANCF) can be treated as isoparametric elements, and by analogy to the classical finite element analysis (FEA) are integrated with standard, spatial Gauss-Legendre quadratures. For this reason, the shape of the ANCF beam cross section is restricted only to the shape of rectangle. In this paper, a distinct method of integration of ANCF elements based on continuum mechanics approach is presented. This method allows for efficient analysis of the ANCF beam elements with circular cross section. The integration of element vectors and matrices is performed by separation of the quadrature into the part that integrate along beam axis and the part that integrate in the beam cross section. Then, an alternative quadrature is used to integrate in the circular shape of the cross section. Since the number of integration points in the alternative quadrature corresponds to the number of points in the standard Gaussian quadrature the change in the shape of the cross section does not affects negatively the element efficiency. The presented method was verified using selected numerical tests. They show good relatively agreement with the reference results. Apart from the analysis of the beams with the circular cross section, a possibility of further modifications in the methods of the element integration is also discussed. Due to the fact that locking influence on the convergence of the element is also observed, the methods of locking elimination in the proposed elements are also considered in the paper.
This paper presents a new algorithm that approximates the forces that develop between a human hand and the handles of a climbing wall. A hand-to-handle model was developed using this algorithm for the Open Dynamics Engine physics solver, which can be plugged into a full-body climbing simulation to improve results. The model data are based on biomechanical measurements of the average population presented in previously published research. The main objective of this work was to identify maximum forces given hand orientation and force direction with respect to the climbing wall handles. Stated as a nonlinear programming problem, solution was achieved by applying a stochastic Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The algorithm for force approximation works consistently and provides reasonable results when gravity is neglected. However, including gravity results in a number of issues. Since the weight of the hand is small in relation to the hand-to-handle forces, neglecting gravity does not significantly affect the reliability and quality of the solution.