Abstract
Functionally graded materials have many applications in engineering. Numerical simulation of structures made by these kinds of materials might be challenging since the properties of the materials are variable from point to point. Therefore, a pointwise numerical method may show better performance. In the present study, a mesh and integral free method is applied for the numerical simulation of Saint-Venant torsion problem in the prismatic bars, whose cross sections are made by functionally graded materials. Here, a simple method is presented to calculate the required integrals in the calculation of the torsional rigidity, in the context of a meshfree method. Thanks to the simplicity of the domain discretization in a meshfree method, cracked sections can be discretized simply using scatter nodes. In the presented vectorized formulation, the shear modules are assigned to each point in a section, which makes the procedure suitable for dealing with inhomogeneous sections. A benchmark problem is solved to validate the scheme. Some cracked sections are considered to investigate the effect of the characteristics of cracks in the torsional rigidity of prismatic bars according to their shear module functions.
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