Discrete Analysis for Plate Bending Problems by Using Hybrid-type Penalty Method

In present paper, we have given investigation of the plate bending problem by numerical treatment using hybrid-type penalty method (HPM) based on discontinuous Galerkin method. The HPM assume linear and nonlinear displacement field with rigid displacement, rigid rotation, strain and its gradient in each subdomain and introduce subsidiary condition about the continuity of displacement into the framework of the variational expression with Lagrange multipliers. For this purpose, we accept the Kirchhoff theory, which takes no into account the transversal shear deformation. In first step of the work, we give the equilibrium equations for deformable body in 3D case and as boundary conditions we give geometrical (for displacement field) and kinetic (for surface force) boundary conditions. Secondary we apply Kirchhoff theory to make the displacement field for plate bending problem into the 3D case. For this purpose, we use quadratic form, which includes rigid, linear, and nonlinear parts of displacements. It can define the parameters used in this displacement field as each subdomain independently. We introduce penalty function, which presents strong spring connecting each subdomain. Then we obtain stiffness matrix as every contact surface of each subdomain. The discretization equation of this model becomes a simulteniuos linear equation. The coefficient matrix consists of stiffness in the sub-domain and subsidiary condition on the intersection boundary for the adjacent sub-domain. In this model, it can express the discontinuous phenomenon of hinge etc. without changing degree of freedom. Finally, w