scholarly journals Peridynamic Higher-Order Beam Formulation

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Method ◽  
Cantilever Beam ◽  
Higher Order ◽  
Point Load ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Good Agreement

Abstract In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

Study on Flexibility of Intracranial Vascular Stents Based on the Finite Element Method

2018 ◽  
Vol 35 (4) ◽  
pp. 465-474 ◽  
Author(s):  
L. Liu ◽  
H. Jiang ◽  
Y. Dong ◽  
L. Quan ◽  
Y. Tong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cantilever Beam ◽  
Beam Model ◽  
The Finite Element Method ◽  
Simply Supported Beam ◽  
Bending Deformation ◽  
Vascular Stents ◽  
Simply Supported ◽  
Loading Method

ABSTRACTFlexibility is a particularly important biomechanical property for intracranial vascular stents. To study the flexibility of stent, the following work was carried out by using the finite element method: Four mechanical models were adopted to simulate the bending deformation of stents, and comparative studies were conducted about the distinction between cantilever beam and simply supported beam, as well as the distinction between moment-loading method and displacement-loading method. A complete process as implanting a stent including compressing, expanding and bending was also simulated, for analyzing the effects of compressing and expanding deformation on stent flexibility. At the same time, the effects of the arrangement and the number of bridges on stent flexibility were researched. The results show that: 1. A same flexibility index was obtained from cantilever beam model and simply supported beam model; displacement-loading method is better than moment-loading for simulating the bending deformation of stents. 2. The flexibility of stent with compressing and expanding deformation is lower than that in the initial form. 3. Crossly arranging the neighboring bridges in axial direction, can effectively improve the stent flexibility and reduce the flexibility difference in various bending directions; the bridge number, has proportional non-linear correlation with the stent rigidity as well as the maximum moment required for bending the stent.

Elastica of Cantilever Beam under Two Follower Forces

1997 ◽  
Vol 1 (2) ◽  
pp. 159-165 ◽  
Author(s):  
Wibisono Hartono
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cantilever Beam ◽  
Elastic Analysis ◽  
The Finite Element Method ◽  
Nonlinear Elastic Analysis ◽  
Displacement Theory ◽  
Follower Forces ◽  
Nonlinear Elastic ◽  
Good Agreement

This paper presents a nonlinear elastic analysis of cantilever beam subjected to two follower forces. Those two proportional forces are always perpendicular to the beam axis. The solution of differential equations based on the large displacement theory, known as elastica is obtained with the help of principle of elastic similarity. For comparison purpose, numerical results using the finite element method are also presented and the results show good agreement.

Bending of Simply-Supported Elliptic Plates: B.P.M. Solutions With Second-Order Derivative Boundary Conditions

1989 ◽  
Vol 56 (2) ◽  
pp. 356-363 ◽  
Author(s):  
R. Parnes
Keyword(s):  
Boundary Conditions ◽  
Perturbation Method ◽  
Higher Order ◽  
Point Load ◽  
Second Order ◽  
Boundary Perturbation ◽  
Simply Supported ◽  
Elliptic Plate ◽  
Elliptic Domain ◽  
Boundary Perturbation Method

A higher-order boundary perturbation method (B.P.M.) is formulated to treat a class of problems defined in an elliptic domain with associated boundary conditions expressed in terms of second-order derivatives. The method is applied to study a simply-supported elliptic plate subjected to a central lateral point load. The accuracy is investigated and the B.P.M. solution is found to yield highly accurate results for moderately elliptic domains.

scholarly journals Derivation and optimization of deflection equations for tapered cantilever beams using the finite element method

2020 ◽  
Vol 39 (2) ◽  
pp. 351-362
Author(s):  
M.M. Ufe ◽  
S.N. Apebo ◽  
A.Y. Iorliam
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Cantilever Beam ◽  
Analytical Solutions ◽  
Point Load ◽  
Structural Systems ◽  
The Finite Element Method ◽  
Tapered Cantilever Beam ◽  
Element Method

This study derived analytical solutions for the deflection of a rectangular cross sectional uniformly tapered cantilever beam with varying configurations of width and breadth acting under an end point load. The deflection equations were derived using a numerical analysis method known as the finite element method. The verification of these analytical solutions was done by deterministic optimisation of the equations using the ModelCenter reliability analysis software and the Abaqus finite element modelling and optimisation software. The results obtained show that the best element type for the finite element analysis of a tapered cantilever beam acting under an end point load is the C3D20RH (A 20-node quadratic brick, hybrid element with linear pressure and reduced integration) beam element; it predicted an end displacement of 0.05035 m for the tapered width, constant height cantilever beam which was the closest value to the analytical optimum of 0.05352 m. The little difference in the deflection value accounted for the numerical error which is inevitably present in the analyses of structural systems. It is recommended that detailed and accurate numerical analysis be adopted in the design of complex structural systems in order to ascertain the degree of uncertainty in design. Keywords: Deflection, Finite element method, deterministic optimisation, numerical error, cantilever beam.

Vertical Deflection of Simply Supported Box Beam with Corrugated Steel Webs Including Effects of Shear Lag and Shear Deformation

2012 ◽  
Vol 204-208 ◽  
pp. 1012-1016 ◽  
Author(s):  
Wei Ji ◽  
Shi Zhong Liu
Keyword(s):  
Finite Element Method ◽  
Shear Deformation ◽  
Comprehensive Analysis ◽  
Shear Lag ◽  
The Finite Element Method ◽  
Vertical Deflection ◽  
Simply Supported ◽  
Box Beam ◽  
Box Beams ◽  
Good Agreement

This paper presents an method to solve the vertical deflection of the box beams with corrugated steel webs, considering both the shear lag and shear deformation of corrugated steel webs. The method is deduced by means of the variational principle. The formulas given by this method is simple and practical. Then, a comprehensive analysis on the effects of shear lag and shear deformation of corrugated steel webs is given for a simply supported box beam with corrugated steel webs under uniformly distributed. The results of vertical deflection obtained by this paper are in good agreement with those obtained by the finite element method (FEM) and the model test, respectively.

Feed-Forward Control of a Cracked Simply Supported Beam

2011 ◽  
Author(s):  
Sudhir Kaul
Keyword(s):  
Crack Propagation ◽  
Control Algorithm ◽  
Control Algorithms ◽  
Transverse Displacement ◽  
Control Force ◽  
Simply Supported Beam ◽  
Feed Forward ◽  
Simply Supported ◽  
Crack Location ◽  
Feed Forward Control

This paper demonstrates the use of two feed-forward control algorithms in order to mitigate crack propagation in a simply supported beam with a pre-existing crack. The main objective of the control algorithms is to minimize or reduce transverse deflection at the crack location so as to contain the damage resulting from the pre-existing crack and, thereby, reduce the rate of crack propagation. A point-load sinusoidal excitation, from a known disturbance, is used as the input load acting on the beam. Two control algorithms are used — the first control algorithm computes a control force to eliminate transverse displacement at the crack location resulting from the excitation force, and the second control algorithm minimizes the mean square transverse displacement over a section of the beam that contains the crack. Both the control algorithms are a-causal and assume that the excitation input is completely known a-priori. Simulation results for a simply supported beam are presented and discussed in detail. It is observed that the rate of crack propagation can be significantly reduced by implementing the proposed feed-forward control algorithms, increasing the useful life of the damaged beam. Also, it is found that the transverse displacement over a significant length of the beam can be substantially reduced when the beam response is dominated by a specific mode.

Research on Stiffness Damage of Simply Supported Beam after Fire

2014 ◽  
Vol 1079-1080 ◽  
pp. 135-139
Author(s):  
Dong Fu Zhao ◽  
Mei Liu ◽  
Xiao Ruan Song ◽  
Dan Wang
Keyword(s):  
Fire Test ◽  
Reduction Method ◽  
Concrete Beams ◽  
Experimental Results ◽  
Simply Supported Beam ◽  
Static Test ◽  
Simply Supported ◽  
Damage Degree ◽  
Width Reduction ◽  
Good Agreement

First, a fire test on concrete beams was carried out. Then after the static test of simply supported beam, the phenomena of simply supported beamsbefore and after fire were compared in order to determine the damage degree ofmechanical property. Finally, the width reduction method was proposed tocalculate the stiffness of beam after fire. And the formula applied toengineering practice was also deduced. The comparison of calculation resultsand experimental results was in a good agreement.

Interaction Curves for Shear and Bending of Plastic Beams

1957 ◽  
Vol 24 (3) ◽  
pp. 453-456
Author(s):  
P. G. Hodge
Keyword(s):  
General Formula ◽  
Plane Stress ◽  
Elementary Theory ◽  
Beam Theory ◽  
Present Theory ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Interaction Curves

Abstract Interaction curves are presented for plastic beams subject to combined shear and bending. A general formula is obtained and specific curves are drawn for rectangular and I-sections. A simply supported beam with a concentrated load is considered as an example. The results are compared with those of simple beam theory and with available plane-stress solutions. It is concluded that the elementary theory is adequate for height-to-length ratios of less than 0.1, while the present theory is useful in the range from 0.1 to 1.0.

scholarly journals Cause Analysis and Countermeasures of Through Shakes in Foamed Concrete Subgrade

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Xianbin Huang ◽  
Chenyang Liu ◽  
Yahong Wangren ◽  
Mingxing Wang ◽  
Yujiao Mei ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Underground Water ◽  
Groundwater Table ◽  
Maximum Displacement ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Load Effect ◽  
The Maximum Principle ◽  
Simply Supported ◽  
Foamed Concrete

The paper presents a new type of material—foamed concrete—adopted for expansion subgrade of the expressway. Intriguingly, the irregular through shakes appear on its top. The method combining the engineering case, theoretical analysis, and numerical simulation is employed to analyze its T-shaped and tree-shaped through shake. The research indicates that when the underground water table is high, cracks are easily seen on the top of step-shape foamed concrete due to buoyancy force. Under the concentrated load effect, the maximum displacement of 27.09 mm is observed on the top of the simply supported beam when elastic modulus is 200 MPa. The maximum principle tensile stress of 0.34 MPa also occurs on the top of the simply supported beam when elastic modulus is 200 MPa and 400 MPa, which is greater than tensile strength of foamed concrete of 0.31 MPa and 0.26 MPa at 7 d and 28 d, respectively. Thus, the adoption of a simply supported beam structure fits site through crack. To avert cracks on the top of foamed concrete in high groundwater table, the antibuoyancy measures should be adopted prior to construction of the upper bearing stratum. The study has expanded the application scope of subgrade and enriched theory of foamed concrete filled in high groundwater table, providing a significant reference to similar projects.

Research on the Effect of Bridge Guardrail to Load Distribution

2014 ◽  
Vol 587-589 ◽  
pp. 1608-1613
Author(s):  
Yong Jun Zhou ◽  
Ting Ting Xu ◽  
Yu Zhao ◽  
Min Yang
Keyword(s):  
Load Distribution ◽  
Load Test ◽  
Main Beam ◽  
Triangular Distribution ◽  
Actual Situation ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Main Girder ◽  
Actual Stress ◽  
Good Agreement

In order to study the effect of guardrail to main girder, simply supported beam load test is relied on to measure the deflection of main girder in different conditions, then whether guardrails involved in the stress of main beam or not in theory is analyzed to draw the conclusion that considering the guardrail in stress is closer to the actual stress of bridge and effects on stiffness of main girder are different in lateral bridge. Based on above four hypotheses are proposed and the guardrail along the bridge transverse triangular distribution to the 14% deck is in good agreement with the actual situation according to the equivalent height.

Sign in / Sign up

Export Citation Format

Share Document