Simplified Consistent Load Vector for Non-rectangular Surface Traction in 3D Finite Element Analysis

摘要

In three-dimensional finite element analysis of structures, frequently non-rectangular uniform traction is encountered. During discretization of the continuum in loading area, the elements at boundary of traction are partially covered. A specific function describing the boundary of the traction is mostly required to calculate consistent loads. From given arbitrary shape of the traction, it becomes a difficult task to find its boundary function. Even if the boundary function can be found out by approximation, the calculation of consistent load involves performing integration within variable limits. Often transformation of boundary function to other trigonometric and algebraic functions is necessary to carryout integration. To overcome these difficulties a simple approach has been proposed, in which the arbitrary shaped area of traction is mapped into equivalent rectangular area. Four types of arbitrary shaped traction with known boundary functions have been taken for analysis using 20 nodded brick elements. The results are found quite close for both original shapes and their transformed rectangular shape.