My Challenge in the Development of a Mixed Variational Method in Solid Mechanics

[+] Author and Article Information
Tadahiko Kawai

Professor, Emeritus,  University of Tokyo, Tokyo, Japan

Appl. Mech. Rev 60(2), 51-64 (Mar 01, 2007) (14 pages) doi:10.1115/1.2472382 History:

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Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Stress-strain law and definition of the strain energy A(ε) and complementary strain energy B(σ). c is loading path on σ-ε diagram

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Figure 2

Definition of a beam element and associated coordinate system

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Figure 3

Deformation analysis of a space frame subjected to a horizontal load. (a) Dimensions. (b) Deformation pattern. The force and moment results obtained are shown in Fig. 4.

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Figure 4

Stress analysis of a simple space frame subjected to a horizontal thrust shown in Fig. 3

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Figure 5

Stress distribution on section C-C of a perforated square plate under uniaxial uniform tension.

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Figure 6

One-element solution obtained by Rayleigh-Ritz method on stress concentration problem

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Figure 7

In-plane bending of a cantilever plate due to a boundary shear of a perabolic distribution given by

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Figure 8

In-plane bending analysis of a cantilever plate subjected to a boundary shear of parabolic distribution (divided by square mesh)

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Figure 9

Plate bending problem

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Figure 10

Bending analysis of a simply supported square plate displacement function used: fifth-order polynomials of (x,y)(DOF=21), which is derived from Goursat’s stress function w(x,y)=Re[z¯φ(z)+χ(z)]

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Figure 11

First Eigenvalue analysis for vibration of a simply supported square plate, displacement function used: fifth-order polynomials of (x,y)(DOF=21)

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Figure 12

A triangular element k and their three neighboring elements l=1, 2, 3




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