MODELLING AND SIMULATION OF SOLID MECHANICS PROBLEMS USING ISOGEOMETRIC ANALYSIS

Abstract

The industries such as aerospace, automobile, shipping, and pipelines use a large number of components made of plates, sheets, and shells. These components are acted upon by different kind of loads. These loads generate stresses in the body. Therefore, it is required to study the behaviour of stresses generated within the body in order to understand their behaviour and possible conditions of failure. Sever load conditions develop high stresses in the body which if exceed material strength results in the progressive and in sonic cases catastrophic failure. These failures are associated with surface or near the surface cracks, discontinuities, flaws, inclusions etc. The presence of these factors reduces the resistance of the material to counter the adversities and hence the strength. An existing crack is the most likely reason for failure and therefore, it is important to study the stress distribution in the near crack region to predict the pattern of crack propagation and the failure of the component which result in the heavy loss. To predict the above characteristics, stress intensity factor (SIF) is required to be evaluated accurately. So, different geometries with different types of discontinuities and loading conditions are analyzed. - If the solution contains a discontinuous and non-smooth feature, like high singularities /gradients in stresses and strains, discontinuities in the displacement field, then for these cases, FEM becomes difficult and expensive to get optimal solution and convergences. The use of Extended Finite Element Method (XFEM) can eliminate the problems associated with discontinuities. To further improve the simulation accuracy, model and analysis of complex geometries and i-educe the time of computation a novel approach extended isogeometric analysis (XIGA) is used. In the former methods the modelling of complex geometries very difficult and the results are less accurate due to geometrical approximation errors in comparison to IGA and XIGA. The geometry is defined exactly even at coarsest mesh by using isogeometric analysis. IGA diminishes the en-or in approximating the geometry accurately and also improves the quality of solution. The higher order NURBS basis function improves the accuracy. In the present work, the modelling and simulation of solid mechanics problems would he carried out using this concept. Isogeometric analysis (IGA) is used to address the stress analysis part without the discontinuities and to analyse the different type of geometries with discontinuities like crack, extended isogeometric analysis (XIGA) is used for different type of loading and boundary conditions.