By Alain Curnier (auth.)
This quantity provides an creation to the 3 numerical tools most typically utilized in the mechanical research of deformable solids, viz. the finite point strategy (FEM), the linear generation technique (LIM), and the finite distinction process (FDM). The booklet has been written from the perspective of simplicity and cohesion; its originality lies within the similar emphasis given to the spatial, temporal and nonlinear dimensions of challenge fixing. This ends up in a neat worldwide 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 tools. even if the dialogue pertains to a one-dimensional version, the formalism used is extendable to two-dimensional occasions. bankruptcy five is dedicated to an in depth dialogue of the compact mix of the 3 tools, and includes numerous sections bearing on their laptop implementation. eventually, bankruptcy 6 supplies a generalization to 2 and 3 dimensions of either the mechanical and numerical facets.
For graduate scholars and researchers whose paintings consists of the speculation and alertness of computational sturdy mechanics.
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Extra resources for Computational Methods in Solid Mechanics
JL ... 72) 41 BAR MODEL PROBLEM Since the derivative of the lineic contact force (PA)' is not defined at the integration limits XM, XA and Xc, it would be incorrect to group these four integrals in one single integral over (O,L). 73) The Hneic contact force PA and the virtual displacement derivative w· are well defined at the integration limits XM, XA et XC , even though they are discontinuous at those points. In other words, their jumps are bounded. L) . This is the key step of the approach.
The slip rule associated to the friction criterion thus assumes the form d/lldl! = lar . In the isotropic case, the ellipse becomes a circle defined by Y(f) = IIfll- 56) These expressions confinn the non-linearity of the nominal law as well as the coupling between elastic and viscous effects when defonnations are large. 4 Nonlinear elasto-plasticity Another type of material non-linearity is caused by the appearance of plastic or permanent deformations in ductile materials, such as metals or plastics (polymers), when they are strained beyond their elastic limit. An idealized linearelastic perfectly-plastic material law can be written. 57) (c) where e is the elastic modulus.
56) These expressions confinn the non-linearity of the nominal law as well as the coupling between elastic and viscous effects when defonnations are large. 4 Nonlinear elasto-plasticity Another type of material non-linearity is caused by the appearance of plastic or permanent deformations in ductile materials, such as metals or plastics (polymers), when they are strained beyond their elastic limit. An idealized linearelastic perfectly-plastic material law can be written. 57) (c) where e is the elastic modulus.