Several Studies On Wave Motion Numerical Simulation Of Interior Domain Medium

Wave motion numerical simulation of interior domain medium is an important aspect of large-scale structure-foundation interaction analysis.Based on the finite element-finite difference method and ABAQUS/Explicit integration scheme,this paper studies the propagation law of the wave motion in discrete grid,and puts forward the analysis method of the calculation precision and the scheme of improving the numerical dispersion.Main tasks are as follows:1.The correctness of the ABAQUS/Explicit integration format we assumed is verified.In this paper a new method for the computational accuracy analysis of explicit integration scheme is proposed.This method is applied in the accuracy analysis of ABAQUS/Explicit.One derives the analytical formulae of the two accuracy indexes with frequency,damping ratio and time step.Quantitative analysis of the computation accuracy is also made in the usual range of damping ratio of engineering structures.2.According to the Recursive form which ABAQUS/Explicit applied to the explicit finite element-finite difference method,the transfer function matrix is deduced,and the propagation law of the fluctuation in the discrete finite element network is given.In the absence of damping there is a cut-off frequency,the wave motion whose frequency is greater than the cutoff frequency cannot be propagated.In the case of damping,the wave motion less than the Nyquist frequency can be propagated in a discrete network.The amplitude of the wave motion close to and greater than the cutoff frequency ?u is rapidly decayed.The smaller the value of the time integration step ?t is and the larger the value of the space step?x is,the smaller the cutoff frequency ?u,the faster the high frequency component decays in the wave motion,and the larger the energy consumption of the integration scheme.3.Comparing with the theoretical solution to evaluate the accuracy of the scheme,it is found that the numerical results of the low frequency region are close to the theoretical solution.When the damping coefficient ?is relatively small,the amplitude attenuation term of the numerical solution is not high fitted with the theoretical solution,and the accuracy of the calculation result is improved with the increase of the ? value.4.The dispersion effect is simulated by the phase velocity and the group velocity.When the lumped mass matrix is adopted,the smaller the time step value is,the more obvious the suppression of the high frequency components in the fluctuation,but the dispersion in the fluctuation will increase.When the Consistent mass matrix is used,the smaller the time step At is,the higher the accuracy of the numerical simulation,the smaller the dispersion of the fluctuation.So the choice of time scales for different quality matrix forms is important.When the Consistent mass matrix is adopted,the larger ? is,the larger the fluctuation dispersion of the numerical simulation which is the same as the theoretical fluctuation dispersion law,but the dispersion effect of ? on the lumped mass matrix is opposite.5.The lumped mass matrix and the consistent mass matrix are linearly combined.This method can improve the accuracy of the calculation results and effectively suppress the dispersion,and the optimal linear combination coefficient is 0.5.