By Alain Curnier (auth.)
This quantity offers an creation to the 3 numerical tools most typically utilized in the mechanical research of deformable solids, viz. the finite point process (FEM), the linear generation approach (LIM), and the finite distinction process (FDM). The ebook has been written from the viewpoint of simplicity and harmony; its originality lies within the related emphasis given to the spatial, temporal and nonlinear dimensions of challenge fixing. This ends up in a neat international set of rules.
bankruptcy 1 addresses the matter of a one-dimensional bar, with emphasis being given to the digital paintings precept. Chapters 2--4 current the 3 numerical equipment. even though the dialogue pertains to a one-dimensional version, the formalism used is extendable to two-dimensional events. bankruptcy five is dedicated to a close dialogue of the compact blend of the 3 equipment, and comprises a number of sections touching on their computing device implementation. eventually, bankruptcy 6 offers a generalization to 2 and 3 dimensions of either the mechanical and numerical features.
For graduate scholars and researchers whose paintings consists of the idea and alertness of computational good mechanics.
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Additional resources for Computational Methods in Solid Mechanics
Dividing both sides of the above equation by the volume V AL gives the material stress power per unit of material volume RG = (q/A) (LIL) . By direct identification of the terms (based on the most natural combinations) the nominal stress R = ql A '" P is shown to be conjugate to the deformation gradient F since G = tiL"" F. = = 25 BAR MODEL PROBLEM The stress S is also called the second Piola-Kirchhoff stress. It has no simple geometric interpretation, but can still be regarded as a "material force" (derived from the standard force by means of the deformation gradient inverse), divided by the reference area S = (F-Iq)/ A .
14. The above derivation may seem cumbersome for arriving at such an obvious result, but it has the advantage of being applicable in two- and three-dimensions (see chap. 6). 62) is implicit because the normal to the criterion is erected at the final stress S and the criterion satisfied by this same final stress. 4. 62) after expressing the plastic criterion in terms of strains (rather than stresses) and upon observing that Eli = E - ST Ie in the elastic case. 61). S dS = e dE' E Fig. 15. For the sake of simplicity, the deformations are assumed to remain small and the materials to behave elastically.
This law is attributed to Kirchhoff and S1. Venan1. 7. It can be shown that a linear nominal law cannot be objective in three dimensions. The rheological model for an elastic material is a spring. S=EE E Fig. 7 Suess-strain vs. force-displacement responses 18 Young's modulus, uaditionally denoted E! 49) is the elastic modulus at the origin. 46) of being monotonous in traction and compression. It can be used to model the behavior of rubber, for instance (Fig. 8). The rheological model for a nonlinear elastic material is a spring pierced by an arrow.
Computational Methods in Solid Mechanics by Alain Curnier (auth.)