Non-Time-step-parameter Time Finite Element Methods And Grid Methods For Numerical Modeling Of Elastic Wave Propagation In Dynamics

Vibration and wave motion are the two research fields of the elastodynamics. The development in the research of analytical solutions is not very rapid because of the complexity of the structural patterns and the media, so moat of the problems have to be investigated by numerical methods. Research of numerical simulation methods that are reasonable, effective, high accuracy, low computational cost and ease to program is the highlight field of the elastodynaniics. Based on Gurtin variational principle of displacement model and making use of Laplace transform, the initial value problems of elastodynamics can be change into the ~equivalent?boundary value problems in the Laplace space. Similar to the principle of minimum potential energy used for the conventional boundary value problems, A kind of functional is constructed in the Laplace space. Then, a simple expression of functional with single convolution integral is given by returning functional in the Laplace space back into the real space. Such a simple functional establishes a 損latform?for the constructions of time finite element methods, so a series of research of time finite element methods could be developed. A concept of non-time-step-parameter is put forward in dealing with the stability problem that often arises in the numerical calculation for the initial value problem of dynamics. One or several non-time-step-parameter can be used in the interpolation function for the discretization in time domain, so the stability in the numerical calculation could be controlled effectively. This idea can also be applied to the construction of other unconditional stable algorithms for the structural analysis of dynamic response. Based on the simple expression of functional and combining the idea of non-time-step-parameter used in the interpolation function for the discretization in time domain, some time finite element methods are studied by using some type of interpolation function in time domain. Some time finite clement methods that could be U? used to solve the initial-boundary value problems of dynamics are put forward and obtain some significant conclusions. A new fully numerical modeling algorithm for elastic wave propagation in heterogeneous media is presented. The scheme is called grid method. The method can accurately model the surface topography and inner curved interfaces by using an unstructured mesh and it is flexible in dealing with the free-surface problem for the semi-infinite media; The complex geometrical free-surface boundary conditions are satisfied naturally and they are stable. Grid method can solve the surface topography and inner curved interface problems that the other finite difference methods give rise difficulti s in incorporating surface topography and curved interfaces by using regular grids for the numerical modeling of elastic wave propagation. Similar to the finite element method in discretization of numerical mesh, the grid method is very flexible in incorporating surface topdgraphy and curved interfaces. The conventional regular grid finite-difference methods are not comparable to the grid method in such an aspect. On the other hand, the grid method need not requirements to calculate and store the global stiffness matrix like the finite element methods and it is a kind of explicit scheme, so the memory requirements and computational cost for the algorithm are much less than that of finite e...