Computerized Analysis of Shells - Governing Equations
Abstract
The volume opens with a general discussion of terms in an energy functional which might be the basis from which equations governing stress, stability, and vibration analyses are derived. The energy expression includes strain energy of the shell and discrete stiffeners, kinetic energy of the shell and stiffeners, constraint conditions with Lagrange multipliers, and other terms arising from the change in direction of applied loads during deformation. Brief discussions are included of the coupling effect between bending and extensional energy needed for the analysis of layered composite shells or elastic-plastic shells, nonlinear terms, and the form that the energy expression takes upon discretization of the structure. A section follows in which the energy formulation for stress, stability, and vibration analyses of an elastic curved beam is given, including thermal effects, moderately large rotations, boundary conditions, and distributed and concentrated loads. The matrix notation and type of discretization are introduced here which will later be used for the analysis of shells of revolution. Terms in the local element stiffness, mass, and load- geometric matrices are derived in terms of nodal point displacements, and it is shown how these local matrices are assembled into global matrices. The purpose of the section is to demonstrate the procedure for derivation of the analogous equations and quantities for shells of revolution or more complex structures.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1981
- Accession Number
- ADA111269
Entities
People
- David Bushnell
Organizations
- Lockheed Martin Missiles and Space