Adaptive Meshless LBIEM for the Analysis of 2D Elasticity Problems

Numerical methods of crack analysis for some 2D-elasticity problems with thermal and dynamic loads are considered in this work. The general steps of the algorithm are presented. Some programs are written by Gibian languages in the codes Castem for crack analysis of different structures. Numerical illustrations are realized for the crack dam model, the plate with one and two cracks the plate with crack at the hole subjected to under variable tension of thermal loads. The influence of the temperature, dynamic loads or position of the crack on fracture parameters for these structures are investigated. The given programs may be useful for estimating the failure of dams, tunnels or other structures.

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A COMPARISON BETWEEN NUMERICAL INTEGRATION TECHNIQUES IN MLPG-1 APPLIED TO 2D ELASTICITY PROBLEMS

10.20906/cps/cilamce2017-0188 ◽

2017 ◽

Author(s):

JOAO PEDRO FRANCO DE MELLO ◽

JOSE ANTONIO FONTES SANTIAGO

Keyword(s):

Numerical Integration ◽

Integration Techniques ◽

Elasticity Problems ◽

2D Elasticity

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Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Composite Structures in Cylindrical Bending

Journal of Applied Mechanics ◽

10.1115/1.4003779 ◽

2011 ◽

Vol 78 (6) ◽

Cited By ~ 16

Author(s):

Santosh Kapuria ◽

Poonam Kumari

Keyword(s):

Boundary Conditions ◽

Three Dimensional ◽

Thickness Direction ◽

Kantorovich Method ◽

Cylindrical Bending ◽

Extended Kantorovich Method ◽

Elasticity Problems ◽

Plane Direction ◽

3D Elasticity ◽

2D Elasticity

The extended Kantorovich method originally proposed by Kerr in the year 1968 for two-dimensional (2D) elasticity problems is further extended to the three-dimensional (3D) elasticity problem of a transversely loaded laminated angle-ply flat panel in cylindrical bending. The significant extensions made to the method in this study are (1) the application to the 3D elasticity problem involving an in-plane direction and a thickness direction instead of both in-plane directions in 2D elasticity problems, (2) the treatment of the nonhomogeneous boundary conditions encountered in the thickness direction, and (3) the use of a mixed variational principle to obtain the governing differential equations in both directions in terms of displacements as well as stresses. This approach not only ensures exact satisfaction of all boundary conditions and continuity conditions at the layer interfaces, but also guarantees the same order of accuracy for all displacement and stress components. The method eventually leads to a set of eight algebraic-ordinary differential equations in the in-plane direction and a similar set of equations in the thickness direction for each layer of the laminate. Exact closed form solutions are obtained for each system of equations. It is demonstrated that the iterative procedure converges very fast irrespective of whether or not the initial guess functions satisfy the boundary conditions. Comparisons of the present predictions with the available 3D exact solutions and 3D finite element solutions for laminated cross-ply and angle-ply composite panels under different boundary conditions show a close agreement between them.

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