Large Deflection of Various Functionally Graded Beam Using Shooting Method

2011 ◽  
Vol 110-116 ◽  
pp. 4705-4711 ◽  
Author(s):  
Ali Soleimani
Keyword(s):  
Exact Solution ◽  
Elastic Modulus ◽  
Loading Condition ◽  
Shooting Method ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Longitudinal Direction ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Arbitrary Loading

The equation of large deflection of functionally graded beam subjected to arbitrary loading condition is derived. In this work assumed that the elastic modulus varies by exponential and power function in longitudinal direction. The nonlinear derived equation has not exact solution so shooting method has been proposed to solve the nonlinear equation of large deflection. Results are validated with finite element solutions. The method will be useful toward the design of compliant mechanisms driven by smart actuators. Finally the effect of different elastic modulus functions and loading conditions are investigated and discussed.

Numerical Study of Large Defection of Functionally Graded Beam with Geometry Nonlinearity

2011 ◽  
Vol 403-408 ◽  
pp. 4226-4230
Author(s):  
A. Soleimani ◽  
M. Saadatfar
Keyword(s):  
Elastic Modulus ◽  
Shooting Method ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Numerical Study ◽  
Longitudinal Direction ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Arbitrary Loading ◽  
Geometry Nonlinearity

The equation of large deflection of functionally graded beam subjected to arbitrary loading condition is derived. In this work assumed that the elastic modulus varies by power function in longitudinal direction. The nonlinear derived equation has not exact solution so shooting method has been proposed to solve the nonlinear equation of large deflection. Results of shooting method are validated with finite element solutions. The method will be useful toward the design of compliant mechanisms driven by smart actuators. Finally the effect of different elastic modulus functions and loading conditions are investigated and discussed.

Analytical Solutions for Large Deflections of Functionally Graded Beams Based on Layer-Graded Beam Model

2018 ◽  
Vol 10 (09) ◽  
pp. 1850098 ◽  
Author(s):  
Peng Zhou ◽  
Ying Liu ◽  
Xiaoyan Liang
Keyword(s):  
Intensity Factor ◽  
Analytical Solutions ◽  
Large Deflection ◽  
Yield Criterion ◽  
Functionally Graded ◽  
Beam Model ◽  
Large Deflections ◽  
Transverse Loading ◽  
Functionally Graded Beam ◽  
Gradient Variation

The objective of this paper is to investigate the large deflection of a slender functionally graded beam under the transverse loading. Firstly, by modeling the functionally graded beam as a layered structure with graded yield strength, a unified yield criterion for a functionally graded metallic beam is established. Based on the proposed yielding criteria, analytical solutions (AS) for the large deflections of fully clamped functionally graded beams subjected to transverse loading are formulated. Comparisons between the present solutions with numerical results are made and good agreements are found. The effects of gradient profile and gradient intensity factor on the large deflections of functionally graded beams are discussed in detail. The reliability of the present analytical model is demonstrated, and the larger the gradient variation ratio near the loading surface is, the more accurate the layer-graded beam model will be.

A Methodology for Compliant Mechanisms Design: Part II — Shooting Method and Application

1992 ◽  
Author(s):  
I. Her ◽  
A. Midha ◽  
B. A. Salamon
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Calculation Method ◽  
Shooting Method ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Shooting Methods ◽  
Beam Structures ◽  
Major Task ◽  
A Chain

Abstract A major task envisioned in the design of compliant mechanisms entails analyzing a large-deflection elastica for its deformed configuration, while being subjected to given displacement and force boundary conditions. The accuracy and convergence behavior of a chain calculation method for predicting nonlinear deflections in beam structures is examined. Three shooting methods are implemented to reduce boundary condition closure errors. These methods are evaluated by considering two example problems in compliant mechanisms.

scholarly journals Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 586 ◽  
Author(s):  
Ali Shariati ◽  
Dong won Jung ◽  
Hamid Mohammad-Sedighi ◽  
Krzysztof Kamil Żur ◽  
Mostafa Habibi ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Critical Velocity ◽  
Natural Frequencies ◽  
Longitudinal Direction ◽  
Variable Density ◽  
Functionally Graded ◽  
Dynamic Configuration ◽  
Stability Maps ◽  
Gradient Parameter ◽  
The Stability

In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler–Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.

Comparison of Post-Buckling Behaviors of a S-S FGM Beam under Conservative and Non-Conservative Distributed Forces

2011 ◽  
Vol 250-253 ◽  
pp. 266-270
Author(s):  
Qing Lu Li ◽  
Shi Rong Li
Keyword(s):  
Deformation Theory ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Conservative System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Beam ◽  
Post Buckling ◽  
Fgm Beam ◽  
Distributed Forces

Based on the large deformation theory and considering the axial extension of the beam, the governing equations of post-buckling of a simply supported elastic FGM beam subjected to conservative and non-conservative distributed forces were established. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using shooting method, the nonlinear boundary-value problem was solved numerically and the equilibrium paths as well as the post- buckling configurations of the deformed beam were presented. A comparison between the results of conservative system and that of non-conservative systems were given. The results shows that the features of the equilibrium paths of the the functionally graded beam under non-conservative are evidently different from those to a conservative one.

scholarly journals Large deflection analysis of nanocomposite cylindrical shell subjected to internal pressure

2020 ◽  
Author(s):  
E. Rahimi ◽  
M.E. Golmakani ◽  
M. Sadeghian
Keyword(s):  
Cylindrical Shell ◽  
Internal Pressure ◽  
Large Deflection ◽  
Volume Fraction ◽  
Geometrical Nonlinearity ◽  
Longitudinal Direction ◽  
Functionally Graded ◽  
Various Boundary Conditions ◽  
Reinforced Composite ◽  
Deflection Analysis

Abstract In this work, large deflection behavior of a functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shell under internal pressure is studied. The composite cylindrical shell reinforced along the longitudinal direction and made from a polymeric matrix. Based on first-order shear deformation shell theory (FSDT) and von Kármán geometrical nonlinearity, the set of governing equations are derived. Using the dynamic relaxation (DR) technique, these systems of equations are solved for various boundary conditions and the roles of volume fraction of CNTs, CNTs distributions and geometrical ratios are examined on the responses.

Large deflection of flexible tapered functionally graded beam

2011 ◽  
Vol 27 (5) ◽  
pp. 767-777 ◽  
Author(s):  
A. R. Davoodinik ◽  
G. H. Rahimi
Keyword(s):  
Large Deflection ◽  
Functionally Graded ◽  
Functionally Graded Beam
Sign in / Sign up

Export Citation Format

Share Document