The stress resultants of a thin plate, such as membrane forces, shear forces and moments, can be calculated through the 3-dimensional elasticity. Plates are indispensable in ship building, automobile, and aerospace industries. Typical examples in civil engineering structures are floor and foundation slabs, lock-gates, thin retaining walls, bridge decks and slab bridges. Moreover, to demonstrate the effectiveness of our method, results of the proposed method are compared with existing results for various shapes of plates with variety of boundary conditions and loads.Ī large number of structural components in engineering can be classified as plates. We also prove error estimates for the proposed meshfree methods.

In this paper, by using generalized product partition of unity, introduced by Oh et al., we introduce meshfree particle methods in which approximation functions have high order polynomial reproducing property and the Kronecker delta property.

Meshfree methods have the advantage of constructing smooth approximation functions, however, most of the earlier works on meshfree methods for plate problems used either moving least squares method with penalty method or coupling FEM with meshfree method to deal with essential boundary conditions. Hence, the conventional finite element method has difficulties to solve the fourth order problems. The vertical displacement of a thin plate is governed by a fourth order elliptic equation and thus the approximation functions for numerical solutions are required to have continuous partial derivatives. In this paper, we are concerned with meshfree particle methods for the solutions of the classical plate model.

Meshfree methods lectures