Study On Generalized Variational Principle In Bridge Structural Analysis-Daubechies Conditional Wavelet

Wavelet theory is a new developing branch in mathematics appeared in the 1980's. In recent years, it is considered as an important breakthrough in methods and tools. And it has been employed in various fields of science and technology and engineering calculation. Especially, Daubechies wavelet has been used the most widely and has the most far-reaching influence because it has obvious superiority in solving some odd state problems, for example, high stress gradient. Wavelet Ritz, wavelet Galerkin and wavelet Finite Element Method (FEM) which are based on Daubechies wavelet have been attached high importance by scholars both at home and abroad in recent yeas. But until now, the application of wavelet theory in structure engineering is far from perfect. Quite a lot difficulties exist in the employing of Daubechies wavelet, such as low computation accuracy of connection coefficients, odd state of displacement transformation matrix, unable to use primary function of higher order vanishing moments, and hard to employ small scaling function space of high accuracy. So how to use wavelet theory, especially Daubechies wavelet to conduct structural computation, improve computation accuracy, overcome the above shortcomings, exploit its special advantages, has significant theoretical importance and obvious practical value.The thesis first briefly introduces the present developing situation of wavelet theory and its application process in numerical calculation; and also systematically introduces the basic theory of wavelet analysis and the mathematic properties of Daubechies wavelet; and then infers the scaling function, wavelet function and correlation derivative, integral, and inner product and the calculating process of existing connection coefficient. Then it clarifies the problem in the existing calculatoin methods of connection coefficients, and also puts forward the effective methods to improve the computation accuracy of connection coefficients.In the present Daubechies wavelet FEM, the displacement transformation matrix has been set between undetermined wavelet coefficients and element internal nodes for the convenience of leading boundary condition. It will transfer the wavelet finite element problem to normal finite element problem, so make the using of wavelet elements convenient. But just because of the existing of displacement transformation matrix, high accuracy computation of Daubechies wavelet elements is hard to achieve, so its application in structural computation has been greatly limited.Based on analyzing the problems existing in traditional Daubechies wavelet FEM, combining traditional Ritz method , Galerkin method with generalized variational principle, this thesis for the first time puts forward conditional wavelet Ritz method and conditional wavelet Galerkin method, and constructs conditional wavelet FEM of element stiffness matrix based on conditional variational principle and Hu-Washizu generalized variational principle. Furthermore, the author also constructs stiffness matrix of conditional wavelet and provide the assembling methods of massive stiffness matrix. So it can be avoided that the computation accuracy is lowered and the calculation result is hard to be convergent for the odd state of transformation matrix.The computation accuracy of wavelet Ritz method and wavelet Galerkin method has been improved so the special'microscopic'property could be fully expressed. An effective method is offered also to solve the problem of high stress gradient and some other odd state problems in engineering. At the same time, the author presents the typical examples to exam the accuracy, stability, calculating speed and its effectiveness for solving the odd state problems like high stress gradient from all respects.Pile is a typical member in bridge structure. The precision of calculating its internal force will affect the whole bridge structure's safety. This thesis for the first time presents a new kind of connection coefficient which can be used in computation of pile foundation; and it also leads the Hu-Washizu principle into Daubechies wavelet FEM to increase the computation accuracy of structural internal force. At last it calculates the typical model of bridge pile foundation using the above methods.The author also writes a great amount of numeric computational sub-programs and programs too, almost include all respects of structural numeric computation using Daubechies wavelet. These programs not only test and verify the correlation results in this thesis, but also lay a strong foundation for expanding the application space of Daubechies wavelet in structural numeric computation.