Bending Analysis of Moderately Thick Arbitrarily Shaped Plates with Point Supports Using Simple Hp Cloud Method

In this paper, a simple hp cloud method is developed for the static analysis of Mindlin plates with various shapes and different boundary conditions. A new application of the hp cloud method, “simple hp cloud method,” is developed based on Kronecker delta property, so that the essential boundary conditions can be imposed directly and as easily as finite element method. Contrary to the hp cloud method, the simple hp cloud method does not require utilizing Lagrange multipliers; hence, the cost of solving algebraic equations is decreased. Shepard functions are used for the partition of unity functions and complete polynomials of order less than or equal to 3 for the enrichment functions part. By using enough order of complete polynomials, the shear locking can be properly controlled. Numerical results are compared against some other solutions to illustrate the accuracy and efficiency of the present method. To show the applications of the simple hp cloud method, deflections and bending moments of quadrilateral, triangular and circular plates with different boundary conditions subjected to transversal distributed loading are considered. In addition, deflections of rectangular and skew plates with point supports are analyzed.