A novel strategy to construct exact structural-property matrices for nonprismatic Timoshenko's frame elements. (15th October 2020)

• Record Type: Journal Article
• Authors: de Araujo, Francisco C.; Ribeiro, Iara S.
• Is Part Of: Computers & structures. Volume 239(2020)
• Publication Date: 2020-10-15
• Subjects: Exact Timoshenko's shape functions -- Nonprismatic frame elements -- Cross sections of arbitrary shapes -- Geometric nonlinear analysis; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2020.106325
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: Timoshenko's frame elements with generically variable rigidity. Novel process for building Timoshenko's shape functions. "Exact" structural-property matrices for frame elements. Reconstitution of the complete equilibrium path in geometric nonlinear analyses of frames. General comments on several nonlinear algorithms. Abstract: Assuming Timoshenko's beam hypothesis, this paper proposes a unified strategy to derive exact finite-element (FE) matrices for framed structures having elements with variable rigidity. Its basic idea is to apply the principle of virtual forces (PVF), at the element level, to obtain a flexibility-based set of equations from which structural-property and nodal-load coefficients can be directly evaluated. The variable physical-geometric characteristics along the frame elements are approximated by polynomials of different orders. For evaluating structural-property coefficients that depend on the deformation of the structure, as e.g. the geometric stiffness coefficients, one employs Timoshenko's consistent shape functions. A novel process for building them under the most general cases of rigidity variation is presented in this paper. In this study, we particularly apply the technique to effect second-order analyses of 2D frames with nonprismatic elements.