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The main contribution of this paper is to propose an IGA formulation to model stationary cracks within orthotropic media by combination of XFEM enrichment functions and level set functions. For modeling cracks in solution field crack face and crack tips are considered separately and the control points that are related to each part are enriched with different approaches. The control points related with the crack face are enriched using the Heaviside enrichment functions. Level set functions are used to distinguish the control points correspond to crack tips and crack face. Stress intensity factors are employed to compare the results of XIGA with other methods. Several numerical examples considering crack inclination angle and material orientation axis are solved to verify the XIGA formulation. The results fairly conform to available methods, however less DOFs are used in XIGA.

In the present study, Gravitational Search Algorithm (GSA) is combined with Finite Element Method (FEM) for optimizing laminated composites vibration behavior. The fiber orientation angle of layers is considered as design variable. The 8-layerd and 12-layerd plates with both of square and rectangular shapes are investigated. Twenty distinct boundary conditions and [Formula: see text] of fiber angle increment are considered. The results of the proposed method are in good agreement with reference methods, and in some cases the GSA-FEM is more efficient. Moreover, the simple structure of GSA and its exploration and exploitation features avoids trapping in a local optimum.