Stephane P. A. Bordas

Ahmad Akbari Rahimabadi, Sundararajan Natarajan, Stephane P. A. Bordas

In this paper, the effect of a centrally located cutout (circular and elliptical) and cracks emanating from the cutout on the free flexural vibration behaviour of functionally graded material plates in thermal environment is studied. The discontinuity surface is represented independent of the mesh by exploiting the partition of unity method framework. A Heaviside function is used to capture the jump in the displacement across the discontinuity surface and asymptotic branch functions are used to capture the singularity around the crack tip. An enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction. The effective properties of the functionally graded material are estimated using the Mori- Tanaka homogenization scheme and the plate kinematics is based on the first order shear deformation theory. The influence of the plate geometry, the geometry of the cutout, the crack length, the thermal gradient and the boundary conditions on the free flexural vibration is numerically studied.

Elena Atroshchenko, Gang Xu, Satyendra Tomar et al.

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces.