This conference paper was submitted for presentation at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

This paper updates research presented at the 2011 NAFEMS World Congress in Boston in the paper identified below. It will present recent work on the vector based approach developed to identify the internal load transfer in two-and three-dimensional elasticity. The vectors in the field are defined by a column of the stress tensor. The theoretical work in the 2011 paper showed that contours plotted through the vector field identified walls across which load did not flow, isolating paths for transfer of load across the domain. Using the stress results from a finite element analysis, load paths were plotted that enhanced the post-processing of finite element results. The new work extends the old approach by allowing the magnitude of the load to vary along the path as load is introduced by a body force. This allows the approach to include gravity loads, and the transfer of moments and shear forces in plates and shells. New work also identifies that load transfer in trusses and frames are a special case where the paths defined by the vectors are parallel to the axes of the members. It is also emphasized that paths need to be investigated for each of the three directions identified by the three columns of the stress tensor in three-dimensional elasticity. A plot of a path for a single load direction (say the x-path for a load applied in the x-direction using vectors defined by the first column of the stress tensor) can miss y-direction and z-direction load transfer due, for example, to bending moments arising from the applied load. New work is also considering the three-dimensional load transfer within laminated composite materials including load transfer between plies in the presence of geometric discontinuities and ply drops. Applications by the authors will include a selection of examples identifying load paths in building frames and static load transfer in bolted joints, curved shells and composite laminates. D. Kelly, G. Pearce, M. Ip, and A. Bassandeh, "Plotting load paths from vectors of finite element stress results," presented at the NAFEMS World Congress 2011, Boston, USA, May 2011. Available at: https://www.nafems.org/publications/resource_center/nwc11_163/