scholarly journals A Trigonometric Analytical Solution of Simply Supported Horizontally Curved Composite I-Beam considering Tangential Slips

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Qin Xu-xi ◽  
Liu Han-bing ◽  
Wu Chun-li ◽  
Gu Zheng-wei
Keyword(s):  
Analytical Solution ◽  
Trigonometric Series ◽  
Beam Theory ◽  
Tangential Direction ◽  
Governing Equations ◽  
Minimum Potential Energy ◽  
Simply Supported ◽  
Horizontally Curved ◽  
Partial Interaction ◽  
Minimum Potential

This paper presents an analytical solution of the simply supported horizontally composite curved I-beam by trigonometric series considering the effect of partial interaction in the tangential direction. Governing equations and boundary conditions are obtained by using the Vlasov curved beam theory and the principle of minimum potential energy. The deflection functions and the Lagrange multiplier functions are expressed as trigonometric series to satisfy the governing equations and the simply supported constraints at both ends. The numerical results of deflections and forces which are obtained by this method are compared with both FEM results and experimental results, and the inaccuracy between the analytical solutions in this paper and the FEM results is small and reasonable.

scholarly journals Analytical Solution of Composite Curved I-Beam considering Tangential Slip under Uniform Distributed Load

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xu-Xi Qin ◽  
He-Ping Chen ◽  
Shu-Juan Wang
Keyword(s):  
Analytical Solution ◽  
Virtual Work ◽  
Beam Theory ◽  
Shell Element ◽  
Tangential Direction ◽  
Distributed Load ◽  
Governing System ◽  
Partial Interaction ◽  
Space Beam Element ◽  
Analytical Expressions

An analytical solution of composite curved I-beam considering the partial interaction in tangential direction under uniform distributed load is obtained. Based on the Vlasov curved beam theory, the global balance condition of the problem has been obtained by means of the principle of virtual work; integrating this by parts, the governing system of differential equations and corresponding boundary conditions have been determined. Analytical expressions for the composite beam considering the partial interaction have been developed. In order to verify the validity and the accuracy of this study, the analytical solutions are presented and compared with other three FEM results using the space beam element and the shell element. The deflection and the tangential slip of the composite curved I-beam are investigated.

Galerkin-Eshelby Meshless Approach to Multiple Inclusion Problem

2017 ◽  
Vol 1144 ◽  
pp. 167-171
Author(s):  
Stanislav Šulc ◽  
Jan Novák
Keyword(s):  
Analytical Solution ◽  
Heterogeneous Material ◽  
Inclusion Problem ◽  
Shape Functions ◽  
Minimum Potential Energy ◽  
Multiple Inclusion ◽  
Single Inclusion ◽  
Homogeneous Matrix ◽  
Minimum Potential ◽  
The Galerkin Method

This paper presents a method of computing perturbation fields in a heterogeneous material composed of multiple ellipsoidal inclusions embedded in homogeneous matrix. The work rests on the renowned Eshelby analytical solution to the single inclusion problem. The strain perturbations, arising from this solution, are used as the shape functions in the Galerkin method, which finds the solution as a combination of these functions with minimum potential energy.

scholarly journals Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Seyyed Amirhosein Hosseini ◽  
Omid Rahmani
Keyword(s):  
Nonlocal Parameter ◽  
Beam Theory ◽  
Opening Angle ◽  
Governing Equations ◽  
Timoshenko Model ◽  
Simply Supported ◽  
Significant Parameter ◽  
Nonlocal Timoshenko Beam Theory ◽  
Fg Nanobeam ◽  
Power Law Index

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction.  The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

scholarly journals Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

2018 ◽  
Author(s):  
Seyyed Amirhosein Hosseini ◽  
Omid Rahmani
Keyword(s):  
Nonlocal Parameter ◽  
Beam Theory ◽  
Opening Angle ◽  
Governing Equations ◽  
Timoshenko Model ◽  
Simply Supported ◽  
Significant Parameter ◽  
Nonlocal Timoshenko Beam Theory ◽  
Fg Nanobeam ◽  
Power Law Index

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction.  The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

scholarly journals Dynamic Analysis of Honeycomb Sandwich Beam with Multiple Debonds

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
B. Saraswathy ◽  
R. Ramesh Kumar ◽  
Lalu Mangal
Keyword(s):  
Analytical Solution ◽  
Transient Analysis ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Beam Length ◽  
Honeycomb Core ◽  
Element Analysis ◽  
Fast Fourier Transform Analysis ◽  
Honeycomb Sandwich ◽  
Nonlinear Transient

Analytical formulation for the evaluation of frequency of CFRP sandwich beam with debond, following the split beam theory, generally underestimates the stiffness, as the contact between the honeycomb core and the skin during vibration is not considered in the region of debond. The validation of the present analytical solution for multiple-debond size is established through 3D finite element analysis, wherein geometry of honeycomb core is modeled as it is, with contact element introduced in the debond region. Nonlinear transient analysis is followed by fast Fourier transform analysis to obtain the frequency response functions. Frequencies are obtained for two types of model having single debond and double debond, at different spacing between them, with debond size up to 40% of beam length. The analytical solution is validated for a debond length of 15% of the beam length, and with the presence of two debonds of same size, the reduction in frequency with respect to that of an intact beam is the same as that of a single-debond case, when the debonds are well separated by three times the size of debond. It is also observed that a single long debond can result in significant reduction in the frequencies of the beam than multiple debond of comparable length.

scholarly journals Analytical solution to bending of stiffened and continuous antisymmetric laminates

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Liecheng Sun ◽  
Issam E. Harik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Displacement Function ◽  
The Other ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Coupling Problem ◽  
Simply Supported ◽  
General Response

AbstractAnalytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

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