Static Analysis of Triangular Plates

This paper may be regarded as a new numerical method for the analysis of triangular thin plates using the natural area coordinates. Previous studies on the solution of triangular plates with different boundary conditions are mostly based on the Rayleigh-Ritz principle which is performed in the Cartesian coordinates. Consequently, manipulation of the geometry and numerical calculation of the integrals are time consuming and tedious. In this paper a new approach is developed to analyze triangular plates by the Ritz method, using interpolation functions in the area coordinates. The geometry is presented in a natural way by mapping a parent triangle and the integrals are evaluated analytically. In this approach, the convergence is always assured due to the completeness of interpolating polynomials. Several examples are presented and the results are compared with other available data.