Abstract
This paper presents a formulation of unified models for beam and shell in curvilinear coordinate system, based on meta-modeling. Traditional structural mechanics is restricted to simple geometries and governing equations are available for a handful number of simple geometries. They are mainly derived based on stress resultants equilibrium of free body diagrams. This gives difficulty in analyzing structural elements with complex geometries analytically and numerically; involving tedious and error prone process. These limita- tions can be eliminated by formulating beam and shell theories for arbitrary geometry defined in curvilinear coordinate system, based on continuum mechanics. Motivated by this improvement, main objective of this work is to develop beam and shell models for arbitrary geometry, using curvilinear coordinate system based on meta-modeling. Meta-modeling guarantees the consistency of the derived beam and shell mod- els with continuum mechanics and tensorial formulation in curvilinear coordinates produces models valid for arbitrary geometries. Governing equations for any specific geometry can be easily obtained simply by substituting the metric tensor of the coordinate system for the problem. This work is mainly based on first order approximations of field variables involved and standard variation process of Hellinger-Reissner func- tional. Some verification tests are done with simple geometries found in literature and it can be clearly seen that they are well matched with literature. Some analytical advantages of derived models are: availabil- ity of governing equations for arbitrary geometries; possible rigorous treatment of material non-linearity; etc. while some numerical advantages are: reduction of per-node number of degrees of freedom; faster convergence of iterative solvers; reduction of number of elements required; increase in accuracy; etc.
