Quadrangular Bézier Patches in Modeling and Modification of the Curvilinear Boundary Surface in 3D Problems of the Theory of Linear Elasticity in PIES

This paper proposes the use of quadrangular Bézier patches to model and modify the shape of the boundary for linear elasticity problems in 3D. The representation of the boundary in this way derives directly from computer graphics and have been analytically included in developed by the authors parametric integral equation systems (PIES). PIES are the modified classical boundary integral equations (BIE) in which the shape of the boundary can be modeled using a wide range of parametric curves and surfaces. The proposed approach eliminates the need for domain and boundary discretization in the process of solving boundary value problems, in contrast to popular traditional methods like FEM and BEM. On the basis of the proposed approach, a computer code has been written and examined through numerical examples.