研究概要

Last update 1999 DEC. 16
超弾性有限要素法による kinking 解析 (Kinking Analysis by Hyper-Elastic Finite Element Method)
日本機械学会論文集 (A 編) , Vol. 61 (No. 583), pp.660-667, (1995)
Abstruct: 'Kinking' is known as an unstable behavior of a twisted slender rod which occurs after the torsional buckling. It is simulated by a hyper-elastic finite element code developed by the authors with hexahedral solid elements. The mechanical characteristics and the criterion of the kinking are successfully discussed. Incompressible constraint to model a rubber-like material is introduced in the simulation by the Lagrange multiplier method and the penalty method. It is found that the former method is computationally more efficient in case extremely large deformation such as kinking is analyzed.
Key Words: Finite Element Method, Torsion, Hyper-Elasticity, Moony-Rivlin Material, Lagrange Multiplier Method, Penalty method
混合型有限要素解の安定条件の数値解析 (Numerical Analysis for Stability Conditions of Mixed Finite Element Solutions)
日本機械学会論文集 (A 編) , Vol. 61 (No. 583), pp.660-667, (1995)
Abstruct: Mixed finite element method has been successfully applied to the analysis of incompressible solid and fluid, shell and beam structures and electromagnetic fields, etc. However it is well known that mixed finite element method may work well in the solution of certain problems but perform very poorly on other problems. In this paper, first, a brief review of the stability conditions for mixed variational principle, which is known as the LBB condition, is given. Then a numerical prediction procedure for the discrete LBB condition which has recently been developed by Malkus (Int. J. Eng. Sci., 19 (1981), 1299) and Chapelle et al. (Compt. & Struct., 47 (1993), 537) is described. Finally the performances of two- and three-dimensional incompressible mixed elements, such as quadrilateral, triangular, hexahedral and tetrahedral elements are systematically investigated based on the discrete LBB condition.
Key Words: Finite Element methods, Numerical Analysis, Computational Mechanics, Mixed Finite Element Method, LBB Condition, Functional Analysis, Numerical Prediction Procedure
超弾性体の混合型有限要素解析に関する基礎的検討 (Mixed Finite Element Analysis of Incompressible Hyperelastic Materials)
日本機械学会論文集 (A 編), Vol. 62 (No. 595), pp.745-752, (1996)
Abstruct In this paper, the Mooney-Rivlin model is employed as the hyperelastic potential function and three methods are discussed for introducing the incompressibility constraint in FE formulation, i.e., the Lagrange multiplier method, the penalty method, and the mixed interpolation with projection, which incorporates the features of the former two methods. Their similarities and differences are also pointed out. Then basic problems are systematically analyzed using these mixed finite elements and performance-based comparisons of resultant numerical behaviors are subsequently applied to clarify the desirable characteristics required to carry out reliable finite element analysis of incompressible hyperelastic materials.
Key Words: Finite Element Method, Numerical Analysis, Computational Mechanics, Mixed Finite Element Method, Hyperelasticity
配管系のラチェッティングに関する研究

東京大学 新領域創成科学研究科 環境学専攻
計算生体力学分野

HOME