| The displacement assumption of traditional finite element is the method of interpolating functions based on polynomials, and the incomplete higher order terms in the polynomial does not improve the accuracy in some cases, instead maybe produces the assumed displacement may include derivative parts, unfortunately the continuity condition between elements is needed. There is adaptive, high stability, high speed, high precision results advantages in the wavelet finite element method based upon the wavelet function. The hybrid stress finite element method is based on modified variational principle. The approach relieves not only the continuity of the unit and relaxes balance requirements, namely the hybrid stress membrane element with a separate assuming displacement field and stress field, but also has high accuracy of stress.The interval of wavelet scale function as the interpolation function is introduced creatively for the hybrid stress element. The new finite element formulation owns the high accuracy of stress and simplifies the procedure of evolutions.Firstly, the characters of the wavelet and scaling functions and the hybrid stress element are analyzed, therefore, a good foundation for the mixed of the wavelet element and the hybrid stress element.Secondly, the hybrid stress equation, and the wavelet scale function as interpolation functions are integrated. Based on the 2, 4 order 0 scale wavelet functions, a type of simple shape function is presented and the process of computer is reduced, and the formulations of the different boundary hypothesis of the stress field and its matrix equations are given. The new wavelet of the hybrid stress is used to model the deflections and stresses of two-dimensional beam and plate with different boundary conditions. A program for present method is written in Mathematica, the numerical results of two-dimensional beam and plate with different boundary conditions are validated by comparing the reference results.Finally, for the need of engineering applications, the modeling of composite laminates is established and the results of the deflection and stress of composite laminates under different boundary conditions are compared with that of the theoretical solution. The results show theerrors are less than 5%. The practicality of the simplified wavelet hybrid element in the paper is testified further by the example of laminates. |
