Some Aspects Regarding Governing Equations of thin Anisotropic Shallow Shells
Tomme: LVII (LXI) Fascicle: 1 | 2011
Pages: 73-86
Abstract text:
Following a procedure similar with those used in case of isotropic shallow shells, the governing equations for membrane and bending state of thin anisotropic shallow shells are derived. For a convenient formulation of governing equations, Hooke’s law is used in the form of resultants stress–strain relations for the entire multy-layered shell, which can be derived on basis of the formulation of the k layer (lamina). The equilibrium equations and kinematic relations are also used. In the most general case of stress–strain state, a coupling between membrane and bending state exists. The obtained equations are particularized for laminated composite shallow shells having an unsymmetrical stacking sequence, made of orthotropic cross-plied layers. In this case the two stress states are uncoupled. Each of the resolvent equations contain two unknowns: the in-plane force resultants function, F, and w – the displace-ment perpendicular on the middle surface of the shell. The system of resolvent equations can be solved by analytic way, using the Fourier series developments of unknown functions and corresponding boundary conditions.
Key Words:
shallow shell; anisotropic material; membrane and bending state; tensile, coupling and bending stiffnesses; governing equations.
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