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

• Published in: Earthquake Engineering and Engineering Vibration Vol. 16; no. 2; pp. 297 - 309
• Main Authors: Jayasinghe, J. A. S. C., Hori, M., Riaz, M. R., Wijerathne, M. L. L., Ichimura, T.
• Format: Journal Article
• Language: English
• Published: Harbin Institute of Engineering Mechanics, China Earthquake Administration 01-04-2017; Springer Nature B.V
• Subjects: Civil Engineering; Continuum mechanics; Control; Conversion; Cross sections; Dynamical Systems; Earth and Environmental Science; Earth Sciences; Finite element analysis; Finite element method; Geotechnical Engineering & Applied Earth Sciences; Ground motion; Mathematical analysis; Mathematical models; Mechanics; Ramps; Seismic engineering; Tunnels; Tunnels (transportation); Vibration; continuum mechanics; meta-modeling theory; finite element method; structural mechanics; solid and beam element models
• ISSN: 1671-3664; 1993-503X
• DOI: 10.1007/s11803-017-0383-z

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.