Efficient modelling of beam-like structures with general non-prismatic, curved geometry. (November 2020)

• Record Type: Journal Article
• Authors: Patni, M.; Minera, S.; Weaver, P.M.; Pirrera, A.
• Is Part Of: Computers & structures. Volume 240(2020)
• Publication Date: 2020-11
• Subjects: Unified formulation -- Finite element -- Non-prismatic -- Tapered sandwich -- Curved structures; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2020.106339
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: Variable kinematics continuum finite element based on Carrera's Unified Formulation. Extension of accurate prediction of 3D elastic fields to structures of general shape. Computationally efficient approach compared to 3D finite element method. Abstract: The analysis of three-dimensional (3D) stress states can be complex and computationally expensive, especially when large deflections cause a nonlinear structural response. Slender structures are conventionally modelled as one-dimensional beams but even these rather simpler analyses can become complicated, e.g. for variable cross-sections and planforms ( i.e. non-prismatic curved beams). In this paper, we present an alternative procedure based on the recently developed Unified Formulation in which the kinematic description of a beam builds upon two shape functions, one for the beam's axis, the other for its cross-section. This approach predicts 3D displacement and stress fields accurately and is computationally efficient in comparison with 3D finite elements. However, current modelling capabilities are limited to the use of prismatic elements. As a means for further applicability, we propose a method to create beam elements with variable planform and variable cross-section, i.e. of general shape. This method employs an additional set of shape functions which describes the geometry of the structure exactly. These functions are different from those used for describing the kinematics and provide local curvilinear basis vectors upon which 3D Jacobian transformation matrices are produced to define non-prismatic elements. The model proposed is benchmarked against 3D finite element analyses, as well as analytical and experimental results available in the literature. Significant computational efficiency gains over 3D finite elements are observed for similar levels of accuracy, for both linear and geometrically nonlinear analyses.