Plane Stress/Strain Analysis by Boundary Integral Equation and Finite Element Methods

摘要

The basis of the finite element method and the boundary integral equation method is derived from the basis differential equations by using a weighted residual technique. The resulting equations form the virtual work statement and the total potential energy of the system and are used to develop the numerical F E method. The BIEM is derived from an extended weighted residual equation which produces a reciprocal statement, known as the Betti-Somigliana formula. A set of known fundamental displacement and traction solutions, which satisfy the differential equation in the domain, are used to form a numerical technique involving only the boundaries. The numerical strategies employed are described and an example highlights the salient points concerning each method.