A meshless local Petrov-Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping.

*(English)*Zbl 1329.74148Summary: This paper is devoted to the geometrically nonlinear analysis of a functionally graded (FG) thick hollow cylinder with Rayleigh damping. The hollow cylinder is subjected to axisymmetric mechanical shock loading on its bounding surfaces. First, the meshless local Petrov-Galerkin (MLPG) method is developed for geometrically nonlinear problems based on total Lagrangian approach. During this process, the local integral equations are obtained using the weak formulation on local sub-domains for the set of governing equations by employing a Heaviside test function. The radial point interpolation method is used to approximate the field variables in terms of nodal displacements. The iterative Newmark/Newton-Raphson method is employed to solve the system of resulting nonlinear equations in suitable time steps. Because of large deformations compared to linear elastic materials, the hyper-elastic neo-Hookean model is considered for the problem. The hollow cylinder is supposed to be in plane strain condition. The properties of the FG cylinder are varied in the thickness direction using the volume fraction that is an exponential function of radius. At the end, to prove the robustness of the proposed method, several numerical tests are performed and effects of relative parameters on the dynamic behavior of the cylinder for various kinds of FGMs are discussed in detail. Findings demonstrate the effectiveness of the presented MLPG method for large deformation problems because of vanishing of the mesh distortion. This paper furnishes a ground to develop the MLPG method for dynamic large deformation problems.

##### MSC:

74J40 | Shocks and related discontinuities in solid mechanics |

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |

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\textit{M. H. Ghadiri Rad} et al., Acta Mech. 226, No. 5, 1497--1513 (2015; Zbl 1329.74148)

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