On the analytical closed-form solution of high-order kinematic models in laminated beam theory

2001 ◽  
Vol 50 (4) ◽  
pp. 919-936 ◽  
Author(s):  
Izhak Sheinman
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Form Solution ◽  
High Order ◽  
Laminated Beam ◽  
Kinematic Models

A closed-form solution for the bending analysis of composite sandwich pipe with compliance core based on high-order sandwich theory

2018 ◽  
Vol 22 (6) ◽  
pp. 1786-1811 ◽  
Author(s):  
I Maleki ◽  
O Rahmani
Keyword(s):  
Closed Form ◽  
Shell Theory ◽  
Variational Principles ◽  
Closed Form Solution ◽  
Form Solution ◽  
High Order ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Nonlinear Distortions ◽  
Flexible Core

In this paper, bending of cylindrical sandwich pipes based on the high-order theory of sandwich structures with flexible core is investigated. The cylindrical sandwich pipe is composed of a flexible core and two composite face sheets. Behavior of the cylindrical sandwich pipe is described by a high-order sandwich shell theory, which explains nonlinear distortions of cross-sectional plane of the flexible core as well as changes in its height. The theory based on variational principles and using an extremely thorough systematic closed-form approach is formulated. In this model, no assumption has been considered for displacement distribution of core components. In this study, stress and displacement of the flexible core are obtained through a three-dimensional elasticity solution and the face sheets are modeled using classical shell theory. Also, a comparison is made in order to verify high-order solution results between a closed-form solution, which is expanded for simply supported boundary conditions and results that are obtained from the commercial finite element method. Finally, influences of physical and geometrical parameters on behavior of the cylindrical sandwich pipe are investigated.

scholarly journals A closed-form solution for free vibration of multiple cracked Timoshenko beam and application

2017 ◽  
Vol 39 (4) ◽  
pp. 315-328
Author(s):  
Nguyen Tien Khiem ◽  
Duong The Hung
Keyword(s):  
Free Vibration ◽  
Closed Form ◽  
Timoshenko Beam ◽  
Crack Depth ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Frequency Equation ◽  
Form Solution ◽  
Mode Shapes ◽  
Timoshenko Beams

A closed-form solution for free vibration is constructed and used for obtaining explicit frequency equation and mode shapes of  Timoshenko beams with arbitrary number of cracks. The cracks are represented by the rotational springs of stiffness calculated from the crack depth.  Using the obtained frequency equation, the sensitivity of natural frequencies to crack of the beams is examined in comparison with the  Euler-Bernoulli beams. Numerical results demonstrate that the Timoshenko beam theory is efficiently applicable not only for short or fat beams but also for the long or slender ones. Nevertheless, both the theories are equivalent in sensitivity analysis of fundamental frequency to cracks and they get to be different for higher frequencies.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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