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 Effects of Fiber Orientation and Material Isotropy on the Analytical Elastic Solution of a Stiffened Orthotropic Panel Subjected to a Combined Loading

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
S. K. Deb Nath
Keyword(s):  
Finite Element ◽  
Composite Materials ◽  
Plane Stress ◽  
Fiber Orientation ◽  
Elastic Field ◽  
Stress Conditions ◽  
Combined Loading ◽  
Potential Approach ◽  
Orthotropic Composite ◽  
Displacement Potential

Using the displacement potential approach of orthotropic composite materials for the plane stress conditions, an orthotropic panel subjected to a combined loading at its right lateral edge is solved. Effects of fiber orientations and material isotropy on the elastic field of an orthotropic panel subjected to a combined loading are discussed. The analytical elastic solutions at different sections of the panel with fiber orientationθ=90° are compared with those of finite element predictions to ensure the reliability of our present solutions.

scholarly journals Eigenvibrations of a simply supported beam with elastically attached load

2018 ◽  
Vol 224 ◽  
pp. 04012 ◽  
Author(s):  
Anton A. Samsonov ◽  
Sergey I. Solov’ev ◽  
Pavel S. Solov’ev
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Eigenvalue Problem ◽  
Approximate Solutions ◽  
Uniform Grid ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Plates And Shells ◽  
The Finite Difference Method ◽  
Theoretical Results

The nonlinear differential eigenvalue problem describing eigenvibrations of a simply supported beam with elastically attached load is investigated. The existence of an increasing sequence of positive simple eigenvalues with limit point at infinity is established. To the sequence of eigenvalues, there corresponds a system of normalized eigenfunctions. To illustrate the obtained theoretical results, the initial problem is approximated by the finite difference method on a uniform grid. The accuracy of approximate solutions is studied. Investigations of the present paper can be generalized for the cases of more complicated and important problems on eigenvibrations of plates and shells with elastically attached loads.

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.

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