A Closed-Form Solution for Thermal Buckling of Cross-Ply Piezolaminated Plates

2016 ◽  
Vol 16 (03) ◽  
pp. 1450112 ◽  
Author(s):  
Mehdi Bohlooly ◽  
Babak Mirzavand
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Ritz Method ◽  
Closed Form Solution ◽  
Laminated Composite ◽  
Composite Plates ◽  
Form Solution ◽  
Thermal Buckling ◽  
Closed Form Solutions ◽  
Piezoelectric Layers

A thermal buckling analysis is presented for simply-supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and subjected to the combined action of thermal load and constant applied actuator voltage. The material properties of the composite and piezoelectric layers are assumed to be functions of temperature. Derivations of the equations are based on the classical laminated plate theory, using the von-Karman nonlinear kinematic relations. The Ritz method is adopted to obtain closed-form solutions for the critical buckling temperature. Numerical examples are presented to verify the proposed method. The effects of the applied actuator voltage, plate geometry and stacking sequence of laminates are investigated.

scholarly journals Thermal Buckling Analysis of Laminated Composite plates with General Elastic Boundary Supports

2020 ◽  
Vol 26 (3) ◽  
pp. 1-17
Author(s):  
Mohammed Basheer Alabas ◽  
Wedad Ibrahim Majid
Keyword(s):  
Boundary Condition ◽  
Fourier Series ◽  
Plate Theory ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Thermal Buckling ◽  
Transverse Displacement ◽  
Rectangular Plates ◽  
Elastic Boundary

In this study, the modified Rayleigh-Ritz method and Fourier series are used to determine the thermal buckling behavior of laminated composite thin plates with a general elastic boundary condition applied to in-plane uniform temperature distribution depending upon classical laminated plate theory(CLPT). A generalized procedure solution is developed for the Rayleigh-Ritz method combined with the synthetic spring technique. The transverse displacement of the orthotropic rectangular plates is not a different term as a new shape expansion of trigonometric series. In this solution approach, the plate transverse deflection and rotation due to bending are developed into principle Fourier series with a sufficient smoothness auxiliary polynomial function, the variable of boundary condition can be easily done by only change the boundary spring stiffness of at the all boundaries of laminated composite plate without achieving any replacement to the solution. The accuracy of the current outcome is verified by comparing with the result obtained from other analytical methods in addition to the finite element method (FEM), so the excellent of this technique is proving during numerical examples.

Stability Analysis of Symmetric Laminated Composite Plates with Geometric Imperfections Under Longitudinal Temperature Gradient

2009 ◽  
Vol 25 (2) ◽  
pp. 161-165 ◽  
Author(s):  
A. Owhadi ◽  
B. Samsam Shariat
Keyword(s):  
Composite Plate ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Thermal Buckling ◽  
Laminated Composite Plates ◽  
Closed Form Solutions ◽  
Longitudinal Temperature Gradient ◽  
Longitudinal Temperature ◽  
Geometrical Imperfections

AbstractThermal buckling behaviour of rectangular laminated composite plates with initial geometrical imperfections is investigated in this article. The equilibrium, stability, and compatibility equations of an imperfect composite plate are derived using the first order shear deformation plate theory. The plate is assumed to be under longitudinal temperature rise. Resulting equations are used to obtain the thermal buckling load of the composite plate in closed-form solutions. The effect of initial imperfections on buckling loads are discussed.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

scholarly journals A New Closed-Form Solution of the Side Abutment Pressure Distribution of Roadway

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liang Cheng ◽  
Yidong Zhang
Keyword(s):  
Plastic Zone ◽  
Pressure Distribution ◽  
Closed Form ◽  
Abutment Pressure ◽  
Closed Form Solution ◽  
Evaluation Process ◽  
Friction Angle ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Roadway Stability

Instability of coal wall is one of the hot-button and difficult issues in the study of coal mine ground control. The shallow side coal of roadway in the coal measures is usually weak and consequently easy to bring about failure. Hence, the side abutment pressure redistributes and dramatically influences the roadway stability. Since the previous closed-form solutions of the side abutment pressure do not take into account all the necessary parameters which include the properties of the coal and the interface between coal and roof/floor, the roadway height, and the support strength, a mechanical model is established based on the equilibrium of the plastic zone, and a new closed-form solution is derived in this paper. Moreover, a numerical investigation is conducted to validate the accuracy of the closed-form solution. The numerical results of the side abutment pressure distribution are in good agreement with the closed-form solution. Afterwards, a parametric analysis of the width of the plastic zone is carried out, and the results show that the width of the plastic zone is nearly negatively linearly correlated with the friction angle and the cohesion of the coal, the interfacial cohesion, and the support strength. By contrast, it is positively linearly correlated with the roadway height and negatively exponentially correlated with the interfacial friction angle. The results obtained in the present study could be useful for the evaluation process of roadway stability.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

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