Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids Part 2: Anisotropic and advanced beam models

• Published in: Computer methods in applied mechanics and engineering Vol. 165; no. 1; pp. 93 - 127
• Main Authors: Petrov, E., Géradin, M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 02-11-1998; Elsevier
• Subjects: Computational techniques; Exact sciences and technology; Finite-element and galerkin methods; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Curved beam; Twisted shape; High strain; Warping; Anisotropic material; Displacement(deformation); Numerical method; Large displacement; Rotation; Monoclinic crystals; Orthotropic material; Finite element method; Three dimensional model; transverse isotropy; Non linear effect; Torsion
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(98)00060-7

Consistent finite element formulations for beams made of anisotropic materials and taking into account non-classic, inhomogeneous torsion have been developed. The formulations are based on a kinematical hypothesis that includes exact solutions for three-dimensional solids under terminal loading. They describe warping of the cross-sections in and out of their planes as well as their rigid displacements and rotations. Their large deformation and geometrically exact description by finite rotations are considered for the cases of monoclinic, orthotropic and transversely isotropic materials. Exact solutions for the solid made from a monoclinic material have been deduced.