scholarly journals Two nodes cusp geometry beam element by using condensed IGA

2019 ◽  
Vol 258 ◽  
pp. 05031
Author(s):  
Buntara Sthenly Gan ◽  
Ay Lie Han
Keyword(s):  
Timoshenko Beam ◽  
Single Point ◽  
Beam Element ◽  
Vertical Shear ◽  
Tangential Displacement ◽  
Control Points ◽  
Element Analysis ◽  
Inertia Effects ◽  
Condensation Method ◽  
Straight Beam

A cusp is a curve which is made by projecting a smooth curve in the 3D Euclidean space on a plane. Such a projection results in a curve whose singularities are self-crossing points or ordinary cusps. Self-crossing points created when two different points of the curves have the same projection at a point. Ordinary cusps created when the tangent to the curve is parallel to the direction of projection on a single point. The study of a cusp geometry beam is more complex than that of a straight beam because the structural deformations of the cusp geometry beam depend also on the coupled tangential displacement caused by the singular geometry. The Isogeometric Approach (IGA) is a computational geometry based on a series of polynomial basis functions used to represent the exact geometry. In IGA, the cusp geometry of the beam element can be modeled exactly. A thick cusp geometry beam element can be developed based on the Timoshenko beam theory, which allows the vertical shear deformation and rotatory inertia effects. The shape of the beam geometry and the shape functions formulation of the element can be obtained from IGA. However, in IGA, the number of equations will increase according to the number of degree of freedom (DOF) at the control points. A new condensation method is adopted to reduce the number of equations at the control points so that it becomes a standard two-node 6-DOF beam element. This paper highlights the application of IGA of a cusp geometry Timoshenko beam element in the context of finite element analysis and proposes a new condensation method to eliminate the drawbacks elevated by the conventional IGA. Examples are given to verify the effectiveness of the condensation method in static and free vibration problems.

The Finite Element Model Study of the Pre-Twisted Timoshenko Beam

2012 ◽  
Vol 446-449 ◽  
pp. 3587-3590
Author(s):  
Chang Hong Chen ◽  
Ying Huang ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Angular Displacement ◽  
Element Model ◽  
Beam Element ◽  
Element Stiffness Matrix ◽  
Straight Beam ◽  
The Relationship ◽  
Timoshenko Beam Element

The paper studies a new mechanical model of pre-twisted Timoshenko beam. But it is different from the conventional Timoshenko straight beam; the proposed new Timoshenko beam element takes separate interpolation polynomial functions both flexure bending displacement and angular displacement. According to the relationship between bending moment and shear, the relationship between of bending displacement and angle displacement is derived, more accurate to consider the effects of shear deformation, come up with a new initial reverse Timoshenko beam element stiffness matrix. Finally, by calculating the pre-twisted rectangle section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Timoshenko beam element stiffness matrix has good accuracy.

Locking Removal Techniques for the Isogeometric Formulation of Curved Beams

2017 ◽  
Vol 1144 ◽  
pp. 109-114
Author(s):  
Edita Dvořáková ◽  
Bořek Patzák
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Beam Element ◽  
Basis Functions ◽  
Shear Locking ◽  
Curved Beams ◽  
Straight Beam ◽  
Discrete Shear Gap ◽  
Thin Beams ◽  
Locking Phenomena

The isogeometric formulation seems to be advantageous especially when it comes to curved geometries such as curved beams and shells. In this paper, the NURBS isogeometric formulation of beam element is presented. The same basis functions are used for both geometry description and unknown approximations so there is no accuracy loss caused by a geometry approximation. The element is based on Timoshenko beam theory which enables the use of the element for both thick and thin beams, nevertheless in case of thin beams the shear-locking phenomena is observed. In the paper it is shown that the reduced integration is insufficient for locking removal and capability of Discrete Shear Gap (DSG) method to unlock the elements is examined. For clear demonstration of locking-removal techniques the implemented element is first tested for the case of straight beam, then the performance is demonstrated on the curved geometry.

The Finite Element Model Research of the Pre-Twisted Beam

2012 ◽  
Vol 188 ◽  
pp. 31-36 ◽  
Author(s):  
Chang Hong Chen ◽  
Ying Huang ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Element Model ◽  
Beam Element ◽  
Euler Beam ◽  
Systematic Analysis ◽  
Straight Beam ◽  
The Relationship ◽  
Twisted Beam ◽  
Timoshenko Beam Element

Based on the traditional mechanical model of straight beam element, the paper makes a systematic analysis and research on the pre-twisted beam finite element numerical model. Firstly, the paper proposed the pre-twisted Euler beam element mode, the mode uses 2 node and 12 freedom degrees, the element axial and torsion displacements use 2 nodes Lagrange interpolation function, bending displacement still use the cubic displacement. Secondly, the paper studies a new pre-twisted Timoshenko beam element mode, the proposed new Timoshenko beam element takes separate interpolation polynomial functions both flexure bending and rotation displacement. According to the relationship between bending moment and shear, the relationship between of bending displacement and angle displacement is derived, which is more accurate to consider the effects of shear deformation. Finally, by calculating the pre-twisted rectangle cantilever beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Timoshenko beam element mode has good accuracy.

Finite Element Analysis of Incremental Sheet Forming for Metal Sheet

2018 ◽  
Vol 783 ◽  
pp. 148-153
Author(s):  
Muhammad Sajjad ◽  
Jithin Ambarayil Joy ◽  
Dong Won Jung
Keyword(s):  
Mechanical Properties ◽  
Sheet Metal ◽  
Tool Path ◽  
Incremental Forming ◽  
Single Point ◽  
Machining Process ◽  
Machining Parameters ◽  
Forming Process ◽  
Element Analysis ◽  
Tool Diameter

Incremental sheet metal forming, is a non-conventional machining process which offers higher formability, flexibility and low cost of production than the traditional conventional forming process. Punch or tool used in this forming process consecutively forces the sheet to deform locally and ultimately gives the target profile. Various machining parameters, such as type of tool, tool path, tool size, feed rate and mechanical properties of sheet metal, like strength co-efficient, strain hardening index and ultimate tensile strength, effects the forming process and the formability of final product. In this research paper, Single Point Incremental Forming was simulated using Dassault system’s Abaqus 6.12-1 and results are obtained. Results of sheet profile and there change in thickness is investigated. For this paper, we simulated the process in abaqus. The tool diameter and rotational speed is find out for the production of parts through incremental forming. The simulation is done for two type of material with different mechanical properties. Various research papers were used to understand the process of incremental forming and its simulation.

Incorporation of Spinal Flexibility Measurements Into Finite Element Analysis

1990 ◽  
Vol 112 (4) ◽  
pp. 481-483 ◽  
Author(s):  
Mack G. Gardner-Morse ◽  
Jeffrey P. Laible ◽  
Ian A. F. Stokes
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Beam Element ◽  
Technical Note ◽  
Element Analysis ◽  
Spinal Motion ◽  
Spinal Flexibility

This technical note demonstrates two methods of incorporating the experimental stiffness of spinal motion segments into a finite element analysis of the spine. The first method is to incorporate the experimental data directly as a stiffness matrix. The second method approximates the experimental data as a beam element.

Finite Element Analysis of Fiber Composite Dental Bridges: The Effect of Length / Depth Ratio and Load Application Method

1999 ◽  
Author(s):  
Michael D. Nowak ◽  
Kim Haser ◽  
A. Jon Goldberg
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mechanical Testing ◽  
Fiber Composite ◽  
Single Point ◽  
Element Analysis ◽  
Elastic Range ◽  
Single Force ◽  
Range Testing ◽  
Fiber Reinforce

Abstract Work is continuing in the evaluation of orthotropic fiber reinforce composites for use in the construction of dental bridges. Finite Element Analysis (FEA) models were constructed based upon mechanical testing of end clamped specimens center loaded with a metal indenter. Various length / depth specimens were evaluated in the elastic range, with a variety of load magnitudes. Separate FEA models utilized single point loading, distributed loading, and the construction of a model indenter. Deflections at the loading point demonstrated that all models presented similar findings to those seen in mechanical testing. The similarity of results between the single loading point and the indenter FEA models suggest that either is reasonable for elastic range testing. The significantly shorter CPU run times for the single force models suggest that this may be the best means by which to model orthotropic fiber reinforced dental composites in the elastic range.

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