An indirect boundary element method for isotropic and orthotropic plates

An indirect boundary element method is presented for analyzing isotropic and orthotropic plates. The integral equation formulation is based on the fundamental solutions and the superposition principle.;For orthotropic plates, the fundamental solutions in a more general form are developed by using the Fourier transform and complex variable calculus. Unlike isotropic materials, there are three forms of fundamental solutions for orthotropic plates depending upon the relationship of the material constants describing the orthotropic materials. The structure in the three forms of the fundamental solutions is identified, and expressed by real and complex variables for different interests. The ideas for solving the isotropic plate problems are directly applied or modified to orthotropic plates. Transversely isotropic and isotropic material behavior is simulated in the test problems.;Numerical results show an excellent correlation with the analytical solutions for clamped and simply supported type plates. The causes of poorer results for shear force boundary conditions are clearly identified for the first time.;The boundary element method starts with the statement of the problem in terms of an integral equation. The integrand in the integral equation is a product of the fundamental solution and an unknown function. The order of continuity that the unknown function must satisfy depends upon the order of singularity in the fundamental solution. In this work, it is verified that the second order singularity present in the fundamental solution requires the continuity of the first derivative of the unknown function. The continuity requirement can be met by using cubic Hermite polynomials. In this work, a limited comparison is made on the use of the Lagrange and Hermite polynomials. Discretization of the problem results in boundary integrals over straight line segments. An iterative technique is used for analytical evaluation of the boundary integrals. The transverse distributed load is incorporated into the formulation through domain integrals. By assuming a constant value for the transverse load over small cells, the domain integrals are transformed to line integrals by the divergence theorem, and evaluated by a similar mean as for the boundary integrals.