Refined 1D Finite Elements for the Analysis of Secondary, Primary, and Complete Civil Engineering Structures

Abstract

This paper proposes the use of an advanced one-dimensional (1D) variable kinematic model to analyze typical civil engineering structures. The model is referred to as component-wise (CW), and it was originally introduced for the analysis of multilayered plate and shell structures. The CW approach is based on the Carrera unified formulation (CUF). CUF can be used for the straightforward development of a large variety of classical and refined beam theories that are able to capture three-dimensional stress/strain states and nonclassical phenomena such as the in-plane warping of the cross section. CUF can be seen as a hierarchical formulation because it has variable kinematic features; 1D models with arbitrarily chosen accuracy can be obtained, including the classical beam theories. CUF models are formulated in terms of fundamental nuclei, whose expressions are formally independent of the adopted hierarchical scheme. Lagrange polynomials are used in the proposed CW models to expand the displacement field of the beam above the cross section. The finite-element method was used in this work to obtain numerical solutions. The conducted numerical investigation shows that CW models can be successfully applied to any geometries with no restrictions on the ratio between the cross-sectional dimensions and the length of the beam. A very short C-shaped beam was therefore used to analyze a classical portal frame. Similarly, analyses of truss structures and a full industrial construction were carried out. Classical beam/plate/solid finite elements as well as combinations of them were used to obtain solutions from a commercial code for comparison purposes. The results show the effectiveness of the CW approach both in terms of accuracy and computational efficiency.