A shear warping kinematic enhancement for fiber beam elements with a damaging cross-section

2021 ◽  
Vol 195 ◽  
pp. 103559
Author(s):  
Sophie Capdevielle ◽  
Stéphane Grange ◽  
Frédéric Dufour ◽  
Cédric Desprez
Keyword(s):  
Cross Section ◽  
Beam Elements

Support-Condition Analyses of Rotating Beams Under Distributed Imbalance Loading

2011 ◽  
Author(s):  
Kai Jokinen ◽  
Erno Keskinen ◽  
Marko Jorkama ◽  
Wolfgang Seemann
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Constant Cross Section ◽  
Support Condition ◽  
Beam Elements

In roll balancing the behaviour of the roll can be studied either experimentally with trial weights or, if the roll dimensions are known, analytically by forming a model of the roll to solve response to imbalance. Essential focus in roll balancing is to find the correct amount and placing for the balancing mass or masses. If this selection is done analytically the roll model used in calculations has significant effect to the balancing result. In this paper three different analytic methods are compared. In first method the mode shapes of the roll are defined piece wisely. The roll is divided in to five parts having different cross sections, two shafts, two roll ends and a shell tube of the roll. Two boundary conditions are found for both supports of the roll and four combining equations are written to the interfaces of different roll parts. Totally 20 equations are established to solve the natural frequencies and to form the mode shapes of the non-uniform roll. In second model the flexibility of shafts and the stiffness of the roll ends are added to the support stiffness as serial springs and the roll is modelled as a one flexibly supported beam having constant cross section. Finally the responses to imbalance of previous models are compared to finite element model using beam elements. Benefits and limitations of each three model are then discussed.

scholarly journals ADJOINT APPROACH SENSITIVITY ANALYSIS OF THIN‐WALLED BEAMS AND FRAMES

2005 ◽  
Vol 11 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Ireneusz Kreja ◽  
Tomasz Mikulski ◽  
Czeslaw Szymczak
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Fem Model ◽  
Static Loads ◽  
Shell Elements ◽  
Beam Elements ◽  
Thin Walled ◽  
The One ◽  
Adjoint Approach ◽  
Open Cross Section

Sensitivity analysis of beams and frames assembled of thin‐walled members is presented within the adjoint approach. Static loads and structures composed of thin‐walled members with the bisymmetrical open cross‐section are considered. The analysed structure is represented by the one‐dimensional model consisting of thin‐walled beam elements based on the classical assumptions of the theory of thin‐walled beams of non‐deformable cross‐section together with superelements applied in place of location of structure nodes, restraints and stiffeners. The results of sensitivity analysis, obtained for the structure model described above, are compared with the results of the detailed FEM model, where the whole structure is discretised with the use of QUAD4 shell elements of the system MSC/NASTRAN.

Evaluation of Mechanical Behaviors of Single-Walled Carbon Nanotubes by Finite Element Analysis

2010 ◽  
Author(s):  
Xiaoxing Lu ◽  
Zhong Hu
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Cross Section ◽  
Plane Deformation ◽  
Element Model ◽  
Element Analysis ◽  
Elliptical Cross ◽  
Beam Elements ◽  
Young’S Moduli ◽  
Walled Carbon Nanotubes

Based on molecular mechanics, a three-dimensional finite element model for armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs) has been developed, in which the carbon nanotubes (CNTs), when subjected to load, behave like space-frame structures. The bending stiffness of the graphite layer has been considered. The potentials associated with the atomic interactions within a CNT were evaluated by the strain energies of beam elements which serve as structural substitutions of covalent bonds. The out-of-plane deformation (inversion) of the bonds was distinguished from the in-plane deformation by considering an elliptical cross-section for the beam elements. The elastic moduli of beam elements are determined by using a linkage between molecular and continuum mechanics. A closed form solution of the sectional properties of the beam element was derived analytically and verified through the analysis of rolling a graphite sheet into a carbon nanotube. This method was validated by its application to a graphene model, and Young’s modulus of the model was found, showing agreement with the known values of graphite. Modeling of the elastic deformation of SWCNTs reveals that Young’s moduli and the shear modulus of CNTs vary with the tube diameter and are affected by their helicity. With increasing tube diameter, Young’s moduli of both armchair and zigzag CNTs are increasing monotonically and approaching to the Young’s modulus of graphite, which are in agreement with the existing theoretical and experimental results. The rolling energy per atom was computed by finite element analysis. By comparing mechanical properties with circular cross section models, it is found that the computational results of the proposed elliptical cross-section model are closer to the results from the atomistic computations. The proposed model is valid for problems where the effect of local bending of the graphite layer in a CNT is significant. This research work shows that the proposed finite element model may provide a valuable tool for studying the mechanical behaviors of CNTs and their integration in nano-composites.

Structural Topology Optimization Using Discete Structural Elements (In the Case of Beam Elements with Ellipsoidal Cross-Section)

2003 ◽  
Vol 2003.13 (0) ◽  
pp. 420-423
Author(s):  
Akihiro TAKEZAWA ◽  
Shinji NISHIWAKI ◽  
Kazuhiro IZUI ◽  
Masataka YOSHIMURA ◽  
Hidekazu NISHIGAKI ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Cross Section ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Structural Elements ◽  
Beam Elements

Torsion Instability of Offshore Cables During Installation

2017 ◽  
Author(s):  
Svein Sævik ◽  
Evgenii Koloshkin
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Design Criteria ◽  
Instability Analysis ◽  
Elastic Case ◽  
Linear Elastic ◽  
Beam Elements ◽  
Flexible Pipes ◽  
Vessel Motion

The present paper addresses torsion instability at the touch down point during installation of offshore cables and flexible pipes. A model for installation instability analysis is established on the basis of standard co-rotated beam elements. The model is validated with respect to the Greenhill analytical solution as well as results obtained for the linear elastic case reported in literature. A case study is then carried out to investigate the effects of cross-section friction moment, inherent torque and vessel motion. This is then used as basis for a proposed design criteria and recommended analysis procedures for evaluating kink formation of offshore flexibles during installation.

Nonlinear Stain of Variable Cross-Section Beam Element Based on Positional FEM

2012 ◽  
Vol 557-559 ◽  
pp. 2371-2374
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Xun Lin Diao ◽  
Xiao Dong Jia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cross Section ◽  
Beam Width ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Nonlinear Fem ◽  
Beam Elements ◽  
Beam Depth

Based on positional finite element method, this paper attempts to find beam elements that can show the characteristics of the variable cross-section beam and can be practically applied. In this paper, the stain on a random point of the variable cross-section beam element is obtained when beam depth changes in a linear or quadratic parabolic way and beam width is fixed. The calculation is different and simpler than the classical nonlinear FEM.

Vibrations in a spatial K-shaped metallic frame: an exact analytical study with experimental validation

2016 ◽  
Vol 23 (19) ◽  
pp. 3147-3161
Author(s):  
C Mei
Keyword(s):  
Cross Section ◽  
Experimental Validation ◽  
Analytical Study ◽  
Torsional Rigidity ◽  
Space Frame ◽  
Bending Vibrations ◽  
Beam Elements ◽  
Out Of Plane ◽  
Vibration Responses ◽  
Shear Distortion

In a spatial K-shaped metallic frame, there exist in- and out-of-plane bending, axial, and torsional vibrations. A wave-based vibration analysis approach is applied to obtain free and forced vibration responses in a space frame. In order to validate the analytical approach, a steel K-shaped space frame was built by welding four beam elements of rectangular and square cross-section together. Bending vibrations are modeled using both the classical Euler–Bernoulli theory and the advanced Timoshenko theory. This allows the effects of rotary inertia and shear distortion, which were neglected in the classical Euler–Bernoulli theory, to be studied. In addition, the effect of torsional rigidity adjustment for structures of rotationally non-symmetric cross-section is also examined.

scholarly journals Static, Vibration, and Transient Dynamic Analyses by Beam Element with Adaptive Displacement Interpolation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Shuang Li ◽  
Jinjun Hu ◽  
Changhai Zhai ◽  
Lili Xie
Keyword(s):  
Cross Section ◽  
Material Properties ◽  
Polynomial Interpolation ◽  
Mass Matrix ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Lumped Mass ◽  
Beam Elements ◽  
Dynamic Analyses ◽  
Interpolation Functions

An approach to analyzing structures by using beam elements is developed with adaptive displacement interpolation functions. First, the element stiffness matrix and equivalent nodal loads are derived on the basis of the equilibrium between nodal forces and section forces rather than the compatibility between nodal deformations and section deformations, which avoids discretization errors caused by the limitation of conventional polynomial interpolation functions. Then, six adaptive element displacement interpolation functions are derived and extended to include several cases, such as beams with variable cross-section, variable material properties, and many different steps in cross-section and/or material properties. To make the element usable in dynamic analyses, consistent mass matrix (CMM) and diagonally lumped mass matrix (LMM) are constructed using the presented adaptive displacement interpolation functions. All these features have made the element elegant, which is tested with a number of simple static, vibration, and dynamic examples to show its accuracy.

Augmented beam elements using unit deflection shapes of the cross section

2016 ◽  
Vol 86 (1-2) ◽  
pp. 135-146 ◽  
Author(s):  
Axel Greim ◽  
Johannes Kreutz ◽  
Gerhard Müller
Keyword(s):  
Cross Section ◽  
Beam Elements ◽  
The Cross

Numerical Examples of Variable Cross-Section Beam Elements

2012 ◽  
Vol 557-559 ◽  
pp. 822-825
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Xun Lin Diao ◽  
Xiao Dong Jia
Keyword(s):  
Exact Solution ◽  
Cantilever Beam ◽  
Cross Section ◽  
Beam Width ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Numerical Examples ◽  
Beam Elements ◽  
Beam Depth

Based on MATLAB platform, program VCBEP (Variable Cross-section Beam Element based on Positional FEM) is compiled, and the cantilever beam with linear profile and the parabolic simple supported beam are calculated. The variable cross-section beam element is proposed to analyze rectangular beam whose beam depth changes in a linear or quadratic parabolic way and beam width is fixed and the exact solution can be obtained.

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