Conjugated Complex Variable Element-free Galerkin Method For Elasticity And Temperature Field Problems

The meshless method is a numerical method that emerged in the middle of 1990 s.The meshless method only needs the information at nodes,and don't discretize the domain into a mesh,there is no mesh movement and mesh distortion,so it has the advantages of wide application range and high precision.These features make the meshless method a hot point and the development trend of numerical methods for science and engineering problems.By introducing the conjugate complex variable moving least-square(CCVMLS)approximation into the EFG method,the conjugate complex variable element-free Galerkin(CCVEFG)method is developed to overcome effectively the disadvantages,such as great computation cost and large numbers of nodes,when the EFG method is used.The advantage of the CCVEFG method is that the trial function of a 2D problem is formed with 1D basis function.Then the unknown coefficients of trial function in the CCVEFG method are fewer than the ones in the EFG method.And then the computational efficiency of the CCVEFG method is greater.The CCVEFG method for elasticity problems is presented in this dissertation.The Galerkin weak form is employed to obtain the equations system,and the penalty method is used to apply the essential boundary conditions,then the CCVEFG method for two-dimensional elasticity problems is established,and the corresponding formulae are obtained,and the corresponding calculation program is compiled,the numerical examples of the three elasticity problems are analyzed numerically,and the calculation parameters in the numerical method are analyzed to determine the reasonable parameter range.This method has the advantages of high precision and good stability.In addition,the use of outsourcing line diagram method,comprehensive inspection and evaluation of the relevant numerical methods of calculation accuracy and computational efficiency,intuitive comparison of the advantages and disadvantages of different numerical methods.The CCVEFG method for temperature field problems is presented in this dissertation.The Galerkin weak form is employed to obtain the equations system,and the penalty method is used to apply the essential boundary conditions,two field variable representation methods are used,in which the field variable in the method I is represented by the real part of the shape function and the field variable in the method II is represented by the real or imaginary part of the test function,then the CCVEFG method for two-dimensional temperature field problems is presented,and the corresponding formulae are obtained,and the corresponding calculation program is compiled,the numerical examples of the three temperature field problems are analyzed numerically,and the calculation parameters in the numerical method are analyzed to determine the reasonable parameter range.This method has the advantages of high precision and good stability,and the method II has higher precision than the method I.