Second-Order Shell Kinematics Implied by Rotation Constraint-Equation |
| |
Authors: | K Wisniewski E Turska |
| |
Institution: | (1) IFTR, Polish Academy of Sciences, Warsaw, Poland |
| |
Abstract: | The paper presents a general methodology of introducing the shell-type variables which is based on the rotation constraint-equation
(RC-equation). The RC-equation is proven to be equivalent to the polar decomposition of the deformation gradient formula,
and the rotations which it yields are interpreted in terms of rotations of vectors of an ortho-normal basis. The deformation
function and rotations are assumed as polynomials of the thickness coordinate ζ, and in this form used in the RC-equation.
Solving this equation, we can express the coefficients of the quadratic deformation function in terms of the following shell-type
variables: (a) the mid-surface position x
0, (b) the constant rotation Q
0, (c) the rotation vector ψ
* for the ζ-dependent rotations, and (d) the normal components U
33
0 and U
33
1 of the right stretching tensor. This new methodology (i) ensures that all shell kinematical variables are consistent with
the RC-equation, which is justified on 3D grounds, (ii) provides a general framework from which various Reissner-type hypotheses
can be obtained by suitable assumptions. As an example, two generalized Reissner hypotheses are derived: one with two normal
stretches, and the other with the in-plane twist and the bubble-like warping parameters.
This revised version was published online in June 2006 with corrections to the Cover Date. |
| |
Keywords: | shell kinematics rotation constraint quadratic deformation function thickness-dependent rotations normal stretches |
本文献已被 SpringerLink 等数据库收录! |
|