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C W Lim - One of the best experts on this subject based on the ideXlab platform.
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accurate analytical approximation to post Buckling of Column with ramberg osgood constitutive law
Applied Mathematical Modelling, 2021Co-Authors: Lihui Chen, Jinhua Cheng, Shaopeng Zheng, C W LimAbstract:Abstract The post-Buckling of a clamped Column made of nonlinear elastic material and subject to axial compression is investigated in this paper. The Ramberg−Osgood type constitutive relation is adopted and it is expanded by using Taylor series. Based on Euler−Bernoulli beam theory, the exact governing equations are expressed in terms of rotation angle. Because the equations contain strongly nonlinear terms that are functions of the rotation angle, analytical solutions are virtually impossible. In this respect, this paper is focused on presenting an alternative method to construct concise yet accurate analytical approximate solutions for post-Buckling of the Ramberg−Osgood Column that is related to large rotation amplitude. The improved harmonic balance method is used to solve the nonlinear governing equations which are simplified via the Maclaurin series expansion and orthogonal Chebyshev polynomials. In addition, numerical solutions by applying the shooting method on the governing equations are obtained for comparison. The second-order analytical approximate solutions presented in this paper show excellent accuracy by comparing with numerical solutions. The analytical approximate method and numerical result presented in this paper can be applied as design guidelines for designing engineering structures that sustain large deformation, such as slender nonlinear compression of aluminum alloy Columns, rods or braces.
Lihui Chen - One of the best experts on this subject based on the ideXlab platform.
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accurate analytical approximation to post Buckling of Column with ramberg osgood constitutive law
Applied Mathematical Modelling, 2021Co-Authors: Lihui Chen, Jinhua Cheng, Shaopeng Zheng, C W LimAbstract:Abstract The post-Buckling of a clamped Column made of nonlinear elastic material and subject to axial compression is investigated in this paper. The Ramberg−Osgood type constitutive relation is adopted and it is expanded by using Taylor series. Based on Euler−Bernoulli beam theory, the exact governing equations are expressed in terms of rotation angle. Because the equations contain strongly nonlinear terms that are functions of the rotation angle, analytical solutions are virtually impossible. In this respect, this paper is focused on presenting an alternative method to construct concise yet accurate analytical approximate solutions for post-Buckling of the Ramberg−Osgood Column that is related to large rotation amplitude. The improved harmonic balance method is used to solve the nonlinear governing equations which are simplified via the Maclaurin series expansion and orthogonal Chebyshev polynomials. In addition, numerical solutions by applying the shooting method on the governing equations are obtained for comparison. The second-order analytical approximate solutions presented in this paper show excellent accuracy by comparing with numerical solutions. The analytical approximate method and numerical result presented in this paper can be applied as design guidelines for designing engineering structures that sustain large deformation, such as slender nonlinear compression of aluminum alloy Columns, rods or braces.
Jinhua Cheng - One of the best experts on this subject based on the ideXlab platform.
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accurate analytical approximation to post Buckling of Column with ramberg osgood constitutive law
Applied Mathematical Modelling, 2021Co-Authors: Lihui Chen, Jinhua Cheng, Shaopeng Zheng, C W LimAbstract:Abstract The post-Buckling of a clamped Column made of nonlinear elastic material and subject to axial compression is investigated in this paper. The Ramberg−Osgood type constitutive relation is adopted and it is expanded by using Taylor series. Based on Euler−Bernoulli beam theory, the exact governing equations are expressed in terms of rotation angle. Because the equations contain strongly nonlinear terms that are functions of the rotation angle, analytical solutions are virtually impossible. In this respect, this paper is focused on presenting an alternative method to construct concise yet accurate analytical approximate solutions for post-Buckling of the Ramberg−Osgood Column that is related to large rotation amplitude. The improved harmonic balance method is used to solve the nonlinear governing equations which are simplified via the Maclaurin series expansion and orthogonal Chebyshev polynomials. In addition, numerical solutions by applying the shooting method on the governing equations are obtained for comparison. The second-order analytical approximate solutions presented in this paper show excellent accuracy by comparing with numerical solutions. The analytical approximate method and numerical result presented in this paper can be applied as design guidelines for designing engineering structures that sustain large deformation, such as slender nonlinear compression of aluminum alloy Columns, rods or braces.
Shaopeng Zheng - One of the best experts on this subject based on the ideXlab platform.
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accurate analytical approximation to post Buckling of Column with ramberg osgood constitutive law
Applied Mathematical Modelling, 2021Co-Authors: Lihui Chen, Jinhua Cheng, Shaopeng Zheng, C W LimAbstract:Abstract The post-Buckling of a clamped Column made of nonlinear elastic material and subject to axial compression is investigated in this paper. The Ramberg−Osgood type constitutive relation is adopted and it is expanded by using Taylor series. Based on Euler−Bernoulli beam theory, the exact governing equations are expressed in terms of rotation angle. Because the equations contain strongly nonlinear terms that are functions of the rotation angle, analytical solutions are virtually impossible. In this respect, this paper is focused on presenting an alternative method to construct concise yet accurate analytical approximate solutions for post-Buckling of the Ramberg−Osgood Column that is related to large rotation amplitude. The improved harmonic balance method is used to solve the nonlinear governing equations which are simplified via the Maclaurin series expansion and orthogonal Chebyshev polynomials. In addition, numerical solutions by applying the shooting method on the governing equations are obtained for comparison. The second-order analytical approximate solutions presented in this paper show excellent accuracy by comparing with numerical solutions. The analytical approximate method and numerical result presented in this paper can be applied as design guidelines for designing engineering structures that sustain large deformation, such as slender nonlinear compression of aluminum alloy Columns, rods or braces.
Tay, Teng Chean - One of the best experts on this subject based on the ideXlab platform.
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Elastic Buckling of Column embedded in a medium
'Nanyang Technological University', 2020Co-Authors: Tay, Teng CheanAbstract:Buckling of Columns is not a fresh topic to be discussed but elastic Buckling of soft elastic Columns is a new field to be studied. Soft robotics are rising in its popularity across different fields including the medical field, food industry, etc. In this research project, the elastic Columns to be embedded in a medium will help to justify the practicality of the lateral reinforcement provided by the surrounding medium. This will help to demonstrate its practical uses in the mechanical structures where utilisation of soft robotics is applicable and biological related research whereby microscopic cells or filaments are surrounded by fluid and other related fields or categories. This Final Year Project will focus on the design and construction of the test rig, elastic Buckling of Columns and elastic Buckling of Columns embedded in a medium. In addition, the research project will revolve around the main parameters including critical Buckling loads, concentration of agar-agar Columns and gelatin medium. Observations are made on the mode shape of the Columns and critical Buckling loads are recorded for every set of experiments. The result will provide an indication of the relationship between the concentration, slenderness, length of specimens and the concentration of the surrounding medium on the critical Buckling loads. Besides, the observation of the mode shape will illustrate the lateral support effectiveness on the Columns by comparing the experiments without the surrounding medium and manipulate the concentration of the cases with the surrounding medium.Bachelor of Engineering (Mechanical Engineering
