Analytical Approximations to Buckling Deformation of the Sandwich Beams Including Transverse Shear

2011 ◽  
Vol 317-319 ◽  
pp. 1783-1786
Author(s):  
Yong Ping Yu ◽  
Lin Zang ◽  
You Hong Sun
Keyword(s):  
Transverse Shear ◽  
Harmonic Balance ◽  
Approximate Solutions ◽  
Beam Equation ◽  
Sandwich Beams ◽  
Nonlinear Beam ◽  
Sandwich Construction ◽  
Analytical Approximations ◽  
Post Buckling ◽  
Approximate Procedure

This paper presents analytical approximate solutions for the initial post-buckling deformation of the sandwich beams including transverse shear. The approximate procedure is based on the nonlinear beam equation (with transverse shear included), by combining the Newton’s method with the method of harmonic balance, we establish analytical approximations to deformation of the sandwich beams. Illustrative examples are presented for a few typical sandwich construction configurations, and it is shown that these approximate solutions are excellent agreement with the “reference” solutions.

Global Buckling and Initial Post-Buckling Behavior of Sandwich Beams Including Transverse Shear

2001 ◽  
Author(s):  
George A. Kardomateas
Keyword(s):  
Transverse Shear ◽  
Compressive Load ◽  
Core Material ◽  
Beam Equation ◽  
Material System ◽  
Sandwich Beams ◽  
Postbuckling Behavior ◽  
Closed Form Solutions ◽  
Sandwich Construction ◽  
Global Buckling

Abstract An asymptotic solution is presented for the buckling and initial postbuckling behavior of sandwich beams. The effect of transverse shear is included and the shear correction is calculated from energy equivalency. The asymptotic procedure is based on the nonlinear beam equation (with transverse shear included) and closed form solutions are derived for the critical loas and for the load and mid-point delamination deflection and axial shortening versus applied compressive load during the initial postbuckling phase. Illustrative results are presented for a few typical sandwich construction configurations, in particular with regard to the effect of face sheet and core material system.

An Asymptotic Solution for the Response of Face-Sheet Delaminations/Debonds Under Compression

2000 ◽  
Author(s):  
George A. Kardomateas ◽  
Haiying Huang
Keyword(s):  
Transverse Shear ◽  
Critical Strain ◽  
Linear Equations ◽  
Face Sheet ◽  
Beam Equation ◽  
System Of Linear Equations ◽  
Postbuckling Behavior ◽  
Nonlinear Beam ◽  
First Order ◽  
Higher Order Terms

Abstract The buckling and initial postbuckling behavior of face-sheet delaminations or face-sheet/core debonds is studied by a perturbation procedure. The procedure is based on the nonlinear beam equation with transverse shear included, and an asymptotic expansion of the load and deformation quantities. First the characteristic equation for the critical load is formulated and this is a nonlinear algebraic equation. Subsequently, the first order load is found from a system of linear equations and the initial postbuckling behavior can thus be studied. The procedure can be easily expanded to the higher order terms. The effect of transverse shear is illustrated with results on the critical strain and the initial postbuckling displacement.

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

2021 ◽  
pp. 146442072110050
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Abdelhak Khechai ◽  
Aicha Bessaim ◽  
Mohammed-Sid-Ahmed Houari ◽  
Aman Garg ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams

In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

Analysis of Rotating Blade Forced Vibration Due to Torsional Excitation Using the Method of Harmonic Balance

2002 ◽  
Author(s):  
B. O. Al-Bedoor ◽  
A. A. Al-Qaisia
Keyword(s):  
Forced Vibration ◽  
Harmonic Balance ◽  
Approximate Solutions ◽  
Coefficient Matrix ◽  
Blade Vibration ◽  
Varying Coefficients ◽  
Rotating Blade ◽  
Method Of Harmonic Balance ◽  
Torsional Excitation ◽  
Truncated Fourier Series

This paper presents an analysis of the forced vibration of rotating blade due to torsional excitation. The model analyzed is a multi-modal forced second order ordinary differential equation with multiple harmonically varying coefficients. The method of Harmonic Balance (HB) is employed to find approximate solutions for each of the blade modes in the form of truncated Fourier series. The solutions have shown multi resonance response for the first blade vibration mode. The examination of the determinant of the harmonic balance solution coefficient matrix for stability purposes has shown that the region between the two resonance points is an unstable vibration region. Numerical integration of the equations is conducted at different frequency ratio points and the results are discussed. This solution provides a very critical operation and design guidance for rotating blade with torsional vibration excitation.

scholarly journals Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Ratchata Theinchai ◽  
Siriwan Chankan ◽  
Weera Yukunthorn
Keyword(s):  
Laplace Transform ◽  
Cantilever Beam ◽  
Adomian Decomposition Method ◽  
Small Deformation ◽  
Approximate Solutions ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam

We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.

Nonlinear stability of sandwich beams with carbon nanotube reinforced faces on elastic foundation under thermal loading

2018 ◽  
Vol 233 (5) ◽  
pp. 1701-1712 ◽  
Author(s):  
Yaser Kiani ◽  
Mostafa Mirzaei
Keyword(s):  
Carbon Nanotube ◽  
Elastic Foundation ◽  
Material Properties ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Ritz Method ◽  
Numerical Results ◽  
Equilibrium Path ◽  
Sandwich Beams ◽  
Post Buckling

In this research, post-buckling response of sandwich beams with carbon nanotube reinforced face sheets subjected to uniform temperature rise loading and resting on a two-parameter elastic foundation is investigated. A single-layer theory formulation based on the first-order shear deformation beam theory is used. Material properties of the media are obtained according to a refined rule of mixtures approach which contains efficiency parameters. Suitable for the large deformations, von-Kármán strains are taken into consideration. The elastic foundation is modelled as the Pasternak model which takes into account the shear interaction of the springs. Material properties of the face sheets are considered to be position and temperature dependent. The governing equations of the system are obtained using the Ritz method for various combinations of clamped, simply supported and sliding supported edges. Post-buckling equilibrium path of the beam is obtained according to an iterative displacement control strategy. Numerical results of the present study are compared with the available data in the open literature. Then, the numerical results are provided to explore the effect of side-to-thickness ratio, volume fraction of carbon nanotube, distribution pattern of carbon nanotube, the ratio of face thickness-to-host thickness, boundary conditions and elastic foundation.

Delamination Suppression in Sandwich Beams Using Translaminar Reinforcements

1999 ◽  
Author(s):  
Brian T. Wallace ◽  
Bhavani V. Sankar ◽  
Peter G. Ifju
Keyword(s):  
Axial Compression ◽  
Sandwich Beam ◽  
Sandwich Beams ◽  
Thickness Direction ◽  
Compression Tests ◽  
Honeycomb Core ◽  
Element Analysis ◽  
Buckling Loads ◽  
Buckling Behavior ◽  
Post Buckling

Abstract The present study is concerned with translaminar reinforcement in a sandwich beam for preventing buckling of a delaminated face-sheet under axial compression. Graphite/epoxy pins are used as reinforcement in the thickness direction of sandwich beams consisting of graphite/epoxy face-sheets and a Aramid honeycomb core. Compression tests are performed to understand the effects of the diameter of the reinforcing pins and reinforcement spacing on the ultimate compressive strength of the delaminated beams. A finite element analysis is performed to understand the effects of translaminar reinforcement on the critical buckling loads and post-buckling behavior of the sandwich beam under axial compression.

scholarly journals Remarks on the existence and decay of the nonlinear beam equation

1994 ◽  
Vol 17 (2) ◽  
pp. 409-412 ◽  
Author(s):  
Jaime E. Mũnoz Rivera
Keyword(s):  
Weak Solution ◽  
Beam Equation ◽  
Nonlinear Beam

We will consider a class of nonlinear beam equation and we will prove the existence and decay weak solution

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