Planar Timoshenko-like model for multilayer non-prismatic beams

Abstract

This paper aims at proposing a Timoshenkolike model for planar multilayer (i.e., non-homogeneous) non-prismatic beams. The main peculiarity of multilayer non-prismatic beams is a non-trivial stress distribution within the cross-section that, therefore, needs a more careful treatment. In greater detail, the axial stress distribution is similar to the one of prismatic beams and can be determined through homogenization whereas the shear distribution is completely different from prismatic beams and depends on all the internal forces. The problem of the representation of the shear stress distribution is overcame by an accurate procedure that is devised on the basis of the Jourawsky theory. The paper demonstrates that the proposed representation of cross-section stress distribution and the rigorous procedure adopted for the derivation of constitutive, equilibrium, and compatibility equations lead to Ordinary Differential Equations that couple the axial and the shear bending problems, but allow practitioners to calculate both analytical and numerical solutions for almost arbitrary beam geometries. Specifically, the numerical examples demonstrate that the proposed beam model is able to predict displacements, internal forces, and stresses very accurately and with moderate computational costs. This is also valid for highly heterogeneous beams characterized by thin and extremely stiff layers.

Efficient modelling of beam-like structures with general non-prismatic, curved geometry

“…The example is adapted from [9], which employs a planar non-prismatic beam model [8] with enhanced stress recovery, based on a rigorous generalisation of Jourawsky's theory. Solving this problem with the UF-SLE model requires two input meshes as shown in Figure 5.…”

“…Trinh and Gan [7] presented an energy based FE method and derived new shape functions for a linearly tapered Timoshenko beam. Balduzzi et al [8] proposed a Timoshenko-like model for planar multilayer non-prismatic beams and solved the problem of the recovery of stress distribution within the cross-section of bi-symmetric tapered steel beams [9].…”

A Model for the T-shaped Beams with Straight Haunches for Uniformly Distributed Load

“…The topic of non-prismatic beams in the last 13 years has aroused great interest among researchers, and the main researchers with different contributions are: Yuksel [13,14], Luévanos-Rojas and Montoya-Ramírez [15], Luévanos-Rojas et al [16], Raju et al [17], Albegmprli et al [18], Luévanos-Rojas [19], Beltempo et al [20], Auricchio et al [21], Luévanos-Rojas et al [22,23], Balduzzi et al [24], Luévanos-Soto and Luévanos-Rojas [25], Balduzzi et al [26], Balduzzi et al [27], Qissab and Salman [28], Rezaiee-Pajand et al [29], Velázquez-Santillán et al [30], Sandoval-Rivas et al [31]. The main objective of this research is to show a model for the T-shaped beams with straight haunches under a uniformly distributed load considering the shear and bending deformations to find the fixedend moments, carry-over and stiffness factors.…”

Modeling the non-trivial behavior of anisotropic beams: A simple Timoshenko beam with enhanced stress recovery and constitutive relations

“…Beam constitutive relations are derived from the stress potential and the outcomes of stress recovery procedure. Such an approach properly embeds anisotropy effects within the beam model and the effectiveness of the proposed constitutive relation derivation path was already demonstrated for non-prismatic and functionally graded material beams [3,1,2,5].…”