Computers & Structures, Vol. 4 pp. 141-754. Rrgnmon Press 1914.Printed in Great Britain AN IMPROVED BOUNDARY-INTEGRAL EQUATION METHOD FOR THREE DIMENSIONAL ELASTIC STRESS ANALYSIS THOMAS A. CRUSE? Department of Mechanical Engineering, Carnegie Institute of Technology, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. Abstract-An improved numerical implementation of the boundary-integral equation method for three dimensional stress analysis is reported. The new implementation models the boundary data as piecewise- linear variations over the boundary segments. As with all boundary-integral equation models, a system of equations relating unknown boundary data to known boundury data is obtained. The new implementation is described mathematically and verified on several simple test problems. In addition the method is used to study a finite fracture specimen used in material testing. The numerical results and computer run times are compared to an earlier version of the boundary-integral equation method. The results show significant improvement in accuracy for comparable run times for most problems. 1. INTRODUCTION THE report concerns the development of an improved version of the Boundary-Integral Equation (BIE) method of stress analysis for three dimensiona elastic bodies. The report deals with the mathematical basis of the improvement, but also compares the improved version of the BIE method to an earlier version [l]. As described in [l], the BJE method of elastic stress analysis is an efficient, yet general method of analysis, The basis of the BIE method is the development of a boundary con- straint equation which relates all boundary displacements to all boundary tractions. The boundary constraint equation applies regardless of the boundary shape (for well defined boundaries) and boundary conditions. For many exterior boundary value problems (infinite body), only the interior boundary need be treated. Thus the dimension of the problem is reduced by one, allowing for efficient modelling schemes for analysis. Due to the reduced dimensionality of the problem, modelling is considerably simpler than for finite element models which discretize the volume of the body. In the previous numerical implementation of the BIE method (referred to herein as 3D1, [I]) the boundary is modelled by piecewise flat triangular segments. Over each segment the boundary data is assumed to be represented by a constant value, referred to the segment centroid. The model corresponds to using the first term in a Taylor series expansion of the boundary data. The improved model, a second generation effort referred to herein as 3D2, makes use of the linear terms from the Taylor series expansion in the plane of the triangular boundary segment. As shown below, the data is by necessity referred to the nodes of the boundary segment map. The next section develops the mathematical basis of the 3D2 model using standard indicial notation with implied summation on repeated indices. The third section describes a series of test problems, many solved by both BIE models: 3Dl and 3D2. The problems t Currently, Pratt and Whitney Aircraft, East Hartford, Connecticut 06108, U.S.A. 741