By M. A. Crisfield
Crisfield's first and moment books are very good resources for someone from varied disiplines. His luck may be attributed to explaining the fabrics of their basic types and to his notations that's effortless to stick with. ranging from 1D nonlinear truss parts to 3D beam-column parts, all options are defined in a similar fashion so when you are into it, one can stick to the textual content. I generally studied his paintings on finite rotations, and arc-length algorithms.
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Extra resources for Advanced Topics, Volume 2, Non-Linear Finite Element Analysis of Solids and Structures
13 REFERENCES [Sl] Sokolnikov, I. , Trrtsor AnccIjtsis, Wiley, New York, London, Sydney (1964). [Y 13 Young, E. Marcel Dekker. New York 1978). 12 More finite element analysis of continua In this chapter, we will apply some of the theory of Chapters 10 and 11 to the finite element analysis of continua. The developments of Chapter 5 were all based on the Green strain and the second Piola-Kirchhoff stresses. To this end, they used the total Lagrangian system in which the stress and strain measures are related to the ‘initial’ configuration.
E = E-G'GJ I/ =E ~ ~ G + ~ G ~+ . . x will be adopted). 38) where i" = i,y are the unit normal vectors defining the rectangular orthogonal base system. (Note: some authors define J as the transpose of the current J . 7 are the covariant components and D,, are the conventional cartesian components. 41) 6 and D is the matrix 34 NON-ORTHOGONALTENSOR COMPONENTS containing the cartesian components D. 41) can be re-expressed as In relation to strains. 43) is written as E,,/ = (G, . ik)(G,,. 8 GREEN'S STRAIN AND THE DEFORMATION GRADIENT We will adopt convected curvilinear coordinates (Figure 1 1 .
87). la) for the symmetric. 1 19) gives the standard relationship t = FSFT. 120) s,, where are components of the stress tensor, S, that is conjugate to the Almansi strain A. 2. 98). 122), which were derived by Hill [H 13, apply only if none of the principal stretches coincide. 83), this relationship is exact for an isotropic response. 122) when we use logCVrather than log,U. In other words we cannot find a stress measure that is work conjugate to log,V. 5, for isotropic conditions we can write the poweriunit initial volume as I/ = t:(log,V)'.