Thermoelastic Analysis Of Ship Structure Using The Cell-based Smoothed Radial Point Interpolation Method

Heat transfer widely exists in people's daily life.Thermal stress analysis is one of the issues that need to be considered in the process of ship structural calculation,which mainly includes the analysis of temperature field,temperature gradient field,thermal strain and thermal stress.For ships and other related large-scale complex structures,it is often difficult to obtain analytical solutions of thermal stress in engineering practice,and usually,commercial software based on the finite element method(FEM)is used to apply the numerical simulation.In the scheme of FEM,linear elements of triangular and tetrahedral elements can be generated in an automotive way,which will save the cost of preprocessing.However,linear elements are generally of low accuracy.Based on linear elements,if a numerical method can improve the accuracy by comparing with the traditional FEM,it would be of great importance for the numerical simulation of engineering heat transfer and thermal stress analysis.In order to solve the above problems existing in FEM,a cell-based smoothed radial point interpolation method(CS-RPIM)has been formulated to analyze thermoelastic problems with complex geometries and complicated boundary conditions.In the scheme of CS-RPIM,linear elements are used to discretize the problem domain and the condensed radial point interpolation method(RPIM)shape functions are created by using both real field nodes and virtual nodes.The CS-RPIM uses the generalized smoothed Galerkin(GS-Galerkin)weak form for constructing discretized system equations and the gradient smoothing operation as welll as numerical integration are performed over the background cells.In this paper,both two-dimensional and three-dimensional basic examples are calculated in detail,and the results calculated by the CS-RPIM method are compared with those by the FEM with the same grid.Under the condition of using same meshes,the CS-RPIM can achieve better accuracy and higher convergence rate in energy norm than the traditional FEM.