Displacement potential solution of a deep stiffened cantilever beam of orthotropic composite material

2007 ◽  
Vol 42 (7) ◽  
pp. 529-540 ◽  
Author(s):  
S. K Deb Nath ◽  
A M Afsar ◽  
S Reaz Ahmed
Keyword(s):  
Composite Material ◽  
Cantilever Beam ◽  
Numerical Solutions ◽  
Elastic Field ◽  
Shear Loading ◽  
Order Partial Differential Equation ◽  
Orthotropic Composite ◽  
Displacement Potential ◽  
Orthotropic Composite Material ◽  
Present Solution

An analytical solution of the elastic field of a deep stiffened cantilever beam of orthotropic composite material is presented in the paper. The cantilever beam is subjected to a parabolic shear loading at its free lateral end and the two opposing longitudinal edges are stiffened. Unidirectional fibre-reinforced composite is considered for the present analysis where the fibres are assumed to be directed along the beam length. Following a new development, the present mixed-boundary-value elastic problem is formulated in terms of a single potential function defined in terms of the associated displacement components. This formulation reduces the problem to the solution of a single fourth-order partial differential equation of equilibrium and is capable of dealing with mixed modes of boundary conditions appropriately. The solution is obtained in the form of an infinite series. Results of different stress and displacement components at different sections of the composite beam are presented numerically in the form of graphs. Finally, in an attempt to check the reliability as well as the accuracy of the present solution, the problem is solved by using two standard numerical methods of solution. A comparison of the results shows that the analytical and numerical solutions of the present problem are in good agreement and thus establishes the soundness as well as the reliability of the present displacement potential approach to solution of the elastic field of orthotropic composite structures.

scholarly journals A Finite Difference Solution of a Simply Supported Beam of Orthotropic Composite Materials Using Displacement Potential Formulation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
S. K. Deb Nath
Keyword(s):  
Composite Materials ◽  
Finite Difference ◽  
Elastic Field ◽  
Elastic Behavior ◽  
Plane Stress Condition ◽  
Simply Supported Beam ◽  
Orthotropic Composite ◽  
Displacement Potential ◽  
Simply Supported ◽  
Potential Formulation

Here an efficient displacement potential formulation based finite difference technique is used to solve the elastic field of a simply supported beam of orthotropic composite materials. A simply supported beam made of orthotropic composite material under uniformly distributed loading is considered and its elastic behaviors under such loading conditions are analyzed considering plane stress condition. The solutions of the problem satisfy the force equilibrium conditions as well as boundary conditions. For understanding the elastic behavior of a simply supported beam, the displacement and stress components of some important sections of the beam are shown graphically. Effects of different orthotropic composite materials on the solutions are also analyzed. Besides, at a particular section of the beam, the comparative analysis of the elastic field is carried out by using the FDM and FEM methods.

scholarly journals Effect of fiber-orientation on stresses at the supporting end of a short cantilever beam of fiber-reinforced composites

2021 ◽  
Author(s):  
Md Jamil Hossain
Keyword(s):  
Cantilever Beam ◽  
Fiber Orientation ◽  
Computational Study ◽  
Elastic Field ◽  
The State ◽  
Fiber Reinforced Composites ◽  
Problem Analysis ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Displacement Potential

The effect of fiber orientation on the state of stress, especially around the supporting end of a short cantilever beam of fiber-reinforced composites is investigated. Two limiting cases of fiber orientation are considered for the composite beam. A displacement potential based finite-difference computational scheme is used to obtain the numerical solution of the elastic field of the problem. Analysis of the results shows that the fiber orientation plays an important role in defining the state of stresses, especially around the supporting end of a cantilever beam. The fiber orientation effect is also identified to be influenced by a number of practical issues like, beam aspect-ratio, supporting condition, type of loading and fiber stiffness. Finally, a comparative analysis of the results with the corresponding FEM solution is included to verify the appropriateness as well as accuracy of the present computational study.

Stress Analysis of Photo-Elastic Orthotropic Composite Material and Measurement Fringe Value of Shear Material

2013 ◽  
Vol 330 ◽  
pp. 12-17
Author(s):  
Yun Jiang ◽  
Hua Dong Zhang ◽  
De Ben Hu ◽  
Xiao Chun Fan
Keyword(s):  
Composite Material ◽  
Cross Section ◽  
Orthotropic Material ◽  
Rectangular Cross Section ◽  
Pure Shear ◽  
Orthotropic Composite ◽  
Orthotropic Composite Material ◽  
Elastic Composite ◽  
Tensile Experiment ◽  
Elastic Shear

Based on the analysis characteristics of orthotropic composite material under antisymmetric force, a new measurement method is established which can independently measure the fringe value of optical shear orthotropic material by pure-shear experiment. Two orthotropic photo-elastic composite material beams with rectangular cross-section which fiber orientation is 0 °, 90 ° respectively are loaded anti-symmetric force, so that the anti-symmetric section is in a pure shear stress state. The fringe value of orthotropic photo-elastic shear composite material is measured . The results agree with three stripe specimens tensile experiment.

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