Uma formulação do método dos elementos de contorno direto de problemas de barras regidos por equações diferenciais de coeficientes variáveis

Abstract

In this work, a direct Boundary Element Method (BEM) formulation for some engineering problems governed by linear differential equation with variable coefficients is established. More specifically, the problems of interest are associated with analysis of five problems of tapered structures. The first two problems are referred to as independent tension compressive problems of straight beans having symmetrical tapering. The remaining problems are associated with axial-bending coupling found in nonsymmetrical tapered beams, symmetric tapered shallow arches, and unsymmetrical tapered shallow arches The BEM solutions here discussed incorporate: a) Euler-Bernoulli and Timoshenko theories for bending effects in beam and shallow arches: b) derivation of the integral equations using Residual Weighted Method and/or Betti's Reciprocal Theorem: c) appropriate mathematical identities are proposed and used to derive the fundamental solutions for tapered beams and shallow arches having generic taper variation; d) domain integrals associated with external distributed loading are transformed into boundary values, e) incorporation into the BEM algebraic equations the domain discontinuities such as intermediate supports, change of the taper law of Cross-section, two or more inclined beams concurrent at a node, change of material) BEM results are presented and compared with analytical and numerical solutions according to their availabilities for different cases of loading, boundary conditions, tapering laws and domain discontinuities.