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Large deformation analyses of space-frame structures, with members of arbitrary cross-section, using explicit tangent stiffness matrices, based on a von Kármán type nonlinear theory in rotated reference frames. (English) Zbl 1231.74038
Summary: This paper presents a simple finite element method, based on simple mechanics and physical clarity, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A co-rotational reference frame, involving the axes of each finitely rotated beam finite-element, is used as the Updated Lagrangian reference frame for the respective element. A von Karman type nonlinear theory of deformation is employed in the co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. An assumed displacement approach is used to derive an explicit expression for the ($$12\times 12$$) symmetric tangent stiffness matrix of the beam element in the co-rotational reference frame. From the finite-displacement vector at each of the two nodes of the beam element, an explicit expression is derived for the matrix of finite rotation of the co-rotational reference frame from the globally-fixed Cartesian reference frame. Thus, this paper provides a text-book example of an explicit expression for the ($$12\times 12$$) symmetric tangent stiffness matrixof a finitely deforming beam element, which can be employed in very simple analyses of large deformations of space-frames.
MSC:
 74B20 Nonlinear elasticity 74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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