Conversion between solid and beam element solutions of finite element method based on meta-modeling theory:development and application to a ramp tunnel structure

摘要

In this study,a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics.The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces.The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics.Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion.Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method.It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method.Further,envelopes of resultant forces which are of primary importance for the purpose of design,are developed for a given ground motion at the end.