Mathematical Elasticity, Vol 27. Studies in Mathematics and its Applications

  • ID: 1764999
  • Book
  • 496 Pages
  • Elsevier Science and Technology
1 of 4
The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.

In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.

Note: Product cover images may vary from those shown
2 of 4
Part A. Linear Plate Theory. 1. Linearly elastic plates. 2. Junctions in linearly elastic multi-structures. 3. Linearly elastic shallow shells in Cartesian coordinates. Part B. Nonlinear Plate Theory. 4. Nonlinearly elastic plates. 5. The von Kármán equations.
Note: Product cover images may vary from those shown
3 of 4

Loading
LOADING...

4 of 4
Unknown, Author
Note: Product cover images may vary from those shown
5 of 4
Note: Product cover images may vary from those shown
Adroll
adroll