A new 3D-beam finite element including non-uniform torsion with the secondary torsion moment deformation effect

In this paper, a new 3D Timoshenko linear-elastic beam finite element including warping torsion will be presented which is suitable for analysis of spatial structures consisting of constant open and hollow structural section (HSS) beams. The analogy between the 2ndorder beam theory (with axial tension) and torsion (including warping) was used for the formulation of the equations for non-uniform torsion. The secondary torsional moment deformation effect and the shear force effect are included into the local beam finite element stiffness matrix. The warping part of the first derivative of the twist angle was considered as an additional degree of freedom at the finite element nodes. This degree of freedom represents a part of the twist angle curvature caused by the bimoment. Results of the numerical experiments are discussed, compared and evaluated. The importance of the inclusion of warping in stress-deformation analyses of closed-section beams is demostrated

Modal analysis of the fgm beam-like structures with effect of the thermal axial force

The modal analysis of the FGM beam-like actuator is presented, where effects of the thermal axial force and the shear force are considered. The temperature load is assumed to be lower as the critical buckling temperature. The longitudinal variation of material properties has been assumed which can be caused by the varying constituent’s volume fraction and the temperature dependence of the constituent’s material properties. Our new FGM beam finite element has been used in the proposed analysis. An influence of the material properties variation and the thermal axial forces on the actuator eigenfrequency and eigenform has been studied and discussed

Linear response of a planar FGM beam with non-linear variation of the mechanical properties

Full paper from the proceedings of SMART2017, which are available at the conference website http://congress.cimne.com/smart2017/.This contribution aims at proposing an effective First order Shear Deformation Theory (FSDT) capable to tackle the non-trivial effects that a continuous variation of the mechanical properties induces on stresses, displacement, and stiffness distributions within a planar beam made of Functionally Graded Material (FGM). In greater detail, the beam model assumes the Timoshenko beam kinematics and it results naturally expressed by six Ordinary Differential Equations (ODEs) considering both cross-section displacements and internal forces as unknowns. Furthermore, exploiting a recently proposed analysis tool, the paper provides also effective tools for the accurate reconstruction of cross-section stress distributions (with special emphasis on shear stresses) and the beam stiffness estimation. A simple numerical example demonstrates that the proposed beam model can catch with good accuracy the main effects induced by variations of the mechanical properties, allowing for a simple and effective modeling of a large class of structures and opening the doors to a new family of enhanced beam models.Austrian Science Funds (FWF

Planar Timoshenko-like model for multilayer non-prismatic beams

This paper aims at proposing a Timoshenko-like 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 thatis 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 almostarbitrary 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.Austrian Science Fund (FWF

Torsional warping eigenmodes of FGM beams with longitudinally varying material properties

The final publication is available via https://doi.org/10.1016/j.engstruct.2018.08.048.Austrian Science Funds (FWF)Slovak Grant Agency: VEG

Effect of Non-Uniform Torsion on Elastostatics of a Frame of Hollow Rectangular Cross-Section

In this paper, results of numerical simulations and measurements are presented concerning the non-uniform torsion and bending of an angled members of hollow cross-section. In numerical simulation, our linear-elastic 3D Timoshenko warping beam finite element is used, which allows consideration of non-uniform torsion. The finite element is suitable for analysis of spatial structures consisting of beams with constant open and closed cross-sections. The effect of the secondary torsional moment and of the shear forces on the deformation is included in the local finite beam element stiffness matrix. The warping part of the first derivative of the twist angle due to bimoment is considered as an additional degree of freedom at the nodes of the finite elements. Standard beam, shell and solid finite elements are also used in the comparative stress and deformation simulations. Results of the numerical experiments are discussed, compared, and evaluated. Measurements are performed for confirmation of the calculated results

Extension of the FGM Beam Finite Element by Warping Torsion

In the contribution, our 3D FGM Timoshenko beam finite element with 12x12 stiffness and mass matrices for doubly symmetric open and closed cross-section [1] is extended by warping torsion effect (non-uniform torsion) to 14x14 finite element matrices. A longitudinal continuous variation of effective material properties is considered by the finite element equations derivation, which can be obtained by homogenization of the spatial varying material properties in real FGM beam. Results of numerical elastostatic non-uniform torsional analysis of the FGM cantilever beam of I-cross-section are presented and the accuracy and effectiveness of the new FGM beam finite element is discussed and evaluated

Modeling the non-trival behavior of anisotropic beams: a simple Tomoshenko beam with enhanced stress recovery and constitutive relations

The final publication is available via https://doi.org/10.1016/j.compstruct.2019.111265.Austrian Science Funds (FWF

Non-prismatic Beams: a Simple and Effective Timoshenko-like Model

The final publication is available via https://doi.org/10.1016/j.ijsolstr.2016.02.017.The present paper discusses simple compatibility, equilibrium, and constitutive equations for a non-prismatic planar beam. Specifically, the proposed model is based on standard Timoshenko kinematics (i.e., planar cross-section remain planar in consequence of a deformation, but can rotate with respect to the beam centerline). An initial discussion of a 2D elastic problem highlights that the boundary equilibrium deeply influences the cross-section stress distribution and all unknown fields are represented with respect to global Cartesian coordinates. A simple beam model (i.e. a set of Ordinary Differential Equations (ODEs)) is derived, describing accurately the effects of non-prismatic geometry on the beam behavior and motivating equation’s terms with both physical and mathematical arguments. Finally, several analytical and numerical solutions are compared with results existing in literature. The main conclusions can be summarized as follows. (i) The stress distribution within the cross-section is not trivial as in prismatic beams, in particular the shear stress distribution depends on all generalized stresses and on the beam geometry. (ii) The derivation of simplified constitutive relations highlights a strong dependence of each generalized deformation on all the generalized stresses. (iii) Axial and shear-bending problems are strictly coupled. (iv) The beam model is naturally expressed as an explicit system of six first order ODEs. (v) The ODEs solution can be obtained through the iterative integration of the right hand side term of each equation. (vi) The proposed simple model predicts the real behavior of non-prismatic beams with a good accuracy, reasonable for the most of practical applications.Austrian Science Fund Cariplo FoundationFoundation Banca del Monte di Lombardia – Progetto Professionalitá Ivano Benchi: Enhancing Competences in Wooden Structure Design 105

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

The final publication is available via https://doi.org/10.1016/j.engstruct.2017.06.023.In this paper, the influence of the variable axial force and of the Secondary Torsion-Moment Deformation-Effect (STMDE) on the deformations of beams due to torsional warping is investigated. The investigation is based on the second-order torsional warping theory of doubly symmetric beams with thin-walled open or closed cross-sections. The effect of the axial force on the torsional stiffness of thinwalled beams is considered according to the second-order torsional warping theory. The solutions of the underlying differential equations are used for setting up the relations, needed for application of the transfer matrix method. They are derived, considering both static and dynamic action. This enables stablishing the local element matrix of the twisted beam in the framework of the Finite Element Method (FEM). The numerical investigation comprises static and modal analyses of thinwalled beams with I cross-sections and rectangular hollow cross-sections. The results are compared with results obtained by the FEM, using solid and beam elements available in standard software.Austrian Science Funds (FWF)Slovak Grant Agencies VEG