Development and application of meta-modeling to establish link between continuum mechanics and structural mechanics

2016 Fiscal Year Final Research Report

• Project/Area Number: 25600153
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Computational science
• Research Institution: The University of Tokyo
• Principal Investigator: HORI MUNEO 東京大学, 地震研究所, 教授 (00219205)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 連続体力学 / 構造力学 / 計算力学 / 有限要素法 / ラグランジュアン / ハミルトニアン

Outline of Final Research Achievements

The objective of the present study is to establish a meta-modeling theory, in order to indicate superiority of solid element FE analysis. Using a Lagrangian of a continuum, we prove that it is possible to make various modeling (posing a mathematical problem) by restring the argument of the Lagrangian and taking variational with respect to the restricted argument. This is the base of the meta-modeling theory.
The meta-modeling theory enables us to use various numerical analysis methods, each of which is to solve a distinct modeling. It is proved that solid element FEM analysis provides an exact solution of a continuum. This implies that other numerical analysis methods such as structure element FE analysis is an approximation of the solid element FE analysis. Comparison of a solid element EF analysis with structure element FE analysis is meaningless in the view point of the meta-modeling theory.

Free Research Field

応用力学