IGA For Spatial Stiffened Shells And Its Application In The Hull Structural Analysis

Finite Element Method(FEM)is one of the most famous and widely used numerical methods nowadays.The general procedure of using FEM is: creating the geometric model,meshing and creating the analysis model,obtaining and solving the equilibrium equation,and post-processing.Complex structures need to be modeled in Computer Aided Design(CAD)systems,while the analysis needs to be performed in Computer Aided Engineer(CAE)systems.The differences of internal databases and geometric expression between the two systems lead to the need for meshing-stage to re-discretize the geometric model expressed by Non-Uniform Rational B-Spline(NUBRS)functions into the analysis model expressed by FEM shape function.This transformation will inevitably lead to the loss of geometric accuracy.The process may also cause the loss of topological relations and the geometric defects such as cracks due to the differences of internal database between CAD and CAE software,which makes it more difficult to mesh the geometry.If we can skip the meshing-stage and bridge the gap between CAD and CAE systems,the efficiency of design and analysis can be greatly improved.Isogeometric analysis(IGA)is proposed to bridge the gap between CAD and CAE systems.IGA takes NURBS \ B-spline as shape functions to discretize domains,and this enables the IGA model to directly inherit the geometric model expressed in the CAD system,without the need for re-discreteness of the geometric model,which fundamentally avoids the loss of geometric accuracy caused by geometric approximation.What’s more,thanks to the highcontinuity of shape functions,IGA patches have the potential to couple non-conforming and non-matched boundary with high precision.This means geometry models with geometric defects can be analyzed directly without the need to fix the model manually,which makes IGA very suitable to analyze complex structures,such as hull structures.If IGA can be introduced into the hull structural analysis,the efficiency of engineers can be greatly improved.It is of great significance to study IGA and its application in hull structural analysis.This paper proposed a IGA framework for the hull structural analysis based on IGA with B-spline.Serval shell elements and beam elements are constructed in the IGA framework,which are: plane shell elements and curvilinear elements based on Kirchhoff-Love shell theory and Reissner-Mindlin shell theory,straight beam element based on Euler-Bernoulli beam theory,and curvilinear beam element based on Timoshenko beam theory.Based on the Nitsche’s method,a weak coupling method for coupling the above-mentioned elements is proposed,which is capable of coupling models with geometric defects and non-conforming meshes.Using the above-mentioned elements and coupling method reasonably according to the characteristics of hull structures,the analysis model can be created at the same time when the geometric model is created.In this way,the time-consuming meshing-stage is skipped,the modeling process is greatly simplified,and the accurate results are obtained with high computational efficiency.The integration of design and analysis is realized.A typical hull block structure is used as numerical example,the accuracy and efficiency of the proposed method and elements are verified by comparing the results of IGA with those of commercial FEM software ANSYS.