Static and free vibration analysis of thin arbitrary-shaped triangular plates under various boundary and internal supports

Abstract Thin triangular plate is one of the common structural members widely used in engineering structures. A weak form numerical method is presented for the static and free vibration analysis of thin arbitrary-shaped triangular plates under various boundary and internal supports. With the help of the sub-parametric technique, the triangular plate domain is first mapped into a regular one with bilinear shape functions and then the discretization is carried out in the regular domain. Gauss quadrature is used to avoid zero of Jacobian determinant at a plate corner. Explicit formulas are worked out for an arbitrary number of nodes. A number of numerical examples are studies. Comparisons show that the presented method is simple and highly accurate. Thus the method may also be used in the design stage for the optimization design of plate shapes as well as lamination sequences of laminated plates.