Geometrically Nonlinear FEM Analysis Of Shell And Three Dimensional Elasto-dynamic Time Domain Direct Integral BEM

The work in this article consists of two parts. The first part is geometrically nonlinear FEM analysis of plates and shells, which was supported by the Research Project of Dynamical Analysis of Aerospace Structure, a key project of National Science Foundation. The second part is the three dimensional elasto-dynamic direct integral BEM in time-domain and its applications, which were the work sponsored by a cooperation project on BEM between Tsinghua University, China, and Kyoto University, Japan.With the special consideration of the deformation characteristic of shells and plates in aerospace structures, a new shell element for large displacement, large rotation and small strain is presented in the first part of the article. The element has 16 nodes, in which 8 nodes are located in the mid-face of the shell, and 8 nodes are virtual nodes. The virtual nodes are used to define the normal of the mid-face in initial and deformed configuration. The displacement mode of the element can depict precisely the rigid body moving and rotation. The relative displacement is obtained by subtracting the convecting displacement from the displacement, which makes it possible to adopt linear strain-displacement relationship in element local coordinate. The geometrically nonlinear shell finite element then is developed.A three dimensional elasto-dynamic direct integral BEM (boundary equation method) in time-domain is presented in the second part of this article. It is the first work in this field. In the present paper, the fundamental singular solution for three dimension elasto-dynamic problems is transformed into a relatively simple form, which has differential terms. When such solution is applied to boundary integral equations, these differentiations can be moved out of the integrals,therefore the integrals are without singularity and can be integrated analytically. Although the present boundary element is spatially constant and temporally linear, a further discussion showed the present method is also suitable for higher temporal interpolation function. Moreover, an idea about the three dimensional elasto-dynamic analytical-numerical integral BEM in time domain is presented finally.As a direct application of the three dimensional elasto-dynamic direct integral BEM in time-domain, the crack opening problem is considered. The crack is idealized as a surface in 3D body and instead of the displacement and traction on crack surface, the crack opening is used as the fundamental variations. The BIE in present model is also non-singular and the algorithm for analytical integration is presented.In the crack identification inverse problem, experiment data will be used for searching true solution, so the dynamical characteristic of the transducer is important. But it is a pity that they are unknown, especially when the transducer is glued to the specimen. The Tikhonov regularization method is used in this article for the identification of the transducer characteristics. Very good result is obtained.Finally the crack identification inverse problem is considered. The optimization method is used for inverse problem and good result is obtained.QI, Hang (Solid Mechanics) Directed by Professor YAO, Zhenhan...