Application Of Wavelet Integral Collocation Method In Large Deflection Bending Of Thin Shallow Shells

As a common building structure in engineering,thin shallow shells have been widely used in various practical problems due to their good mechanical properties,which has attracted scientists’widespread attention.With the development of society and the requirements of engineering construction,many problems in engineering construction involve complex nonlinear factors.Therefore,many scholars have conducted research on the nonlinear problems of shallow shell structures in mechanics.In recent years,wavelet numerical methods have developed rapidly.With faster convergence speed,better computational efficiency,and higher computational accuracy,they have become a powerful tool for solving nonlinear equations,and have been studied and applied by the scholars.This paper investigates the application of wavelet integral collocation numerical method in thin shallow shell problems,and constructs a wavelet solution format for large deflection bending problems of shallow shells.The obtained results of numerical examples are analyzed and discussed,further verifying the feasibility and universality of wavelet integral collocation method.The detail content is as follows:(1)Firstly,the basic theory of wavelet algorithm and the construction method of orthogonal Coiflet wavelet function are described.The calculation method of multiple integral value of Coiflet scaling function is introduced in detail.One-dimensional and multi-dimensional Coiflet wavelet integral approximation schemes for functions in L~2defined on finite intervals is presented,and the high-precision characteristics of wavelet approximation functions and function integrals are verified with several examples.(2)Based on the wavelet approximation theory,the basic idea and solution process of the wavelet integral collocation method are presented in detail.The numerical schemes of the wavelet integral collocation method for one-dimensional and multi-dimensional problems are given respectively.Combined with specific nonlinear numerical examples,the methods have been verified with good accuracy and convergence rate.Based on the analysis and discussion of the basic governing equations for the large deflection bending problem of shallow shells,we have derived a general governing equation for the large deflection bending problem of shallow shells in detail.Combining the wavelet integral collocation method,a wavelet numerical scheme for the large deflection bending problem of shallow shells is deduced.In order to verify the accuracy of the wavelet integral collocation method in solving such problems,we constructed a nonlinear equation system with similar mathematical form of which analytical solutions can be resolved,and further verified the feasibility and high-precision characteristics of the wavelet integral collocation method in solving such equations.Finally,the wavelet integral collocation method is applied to solve the large deflection bending problem of shallow shells.The wavelet numerical results are compared with other classical numerical methods,indicating that the wavelet integral collocation method has advantages of high accuracy and efficiency.This verifies the feasibility and reliability of the wavelet integral collocation method.Further analysis are conducted on the basis of the results,and future work is also discussed.