A. M. Afsar

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

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.

Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media

Abstract This study is concerned with the inverse problem of calculating material distributions intending to realize prescribed apparent fracture toughness in functionally graded material (FGM) coatings around a circular hole in infinite elastic media. The incompatible eigenstrain induced in the FGM coatings after cooling from the sintering temperature, due to mismatch in the coefficients of thermal expansion, is taken into consideration. An approximation method of determining stress intensity factors is introduced for a crack in the FGM coatings in which the FGM coatings are homogenized simulating the nonhomogeneous material properties by a distribution of equivalent eigenstrain. A radial edge crack emanating from the circular hole in the homogenized coatings is considered for the case of a uniform pressure applied to the surfaces of the hole and the crack. The stress intensity factors determined for the crack in the homogenized coatings represent the approximate values of the stress intensity factors for the same crack in the FGM coatings, and are used in the inverse problem of calculating material distributions in the FGM coatings intending to realize prescribed apparent fracture toughness in the coatings. Numerical results are obtained for a TiC/Al 2 O 3 FGM coating, which reveal that the apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media can be controlled within possible limits by choosing an appropriate material distribution profile in the coatings.

Optimum material distributions for prescribed apparent fracture toughness in thick-walled FGM circular pipes

Abstract This study treats the inverse problem of evaluating optimum material distributions intending to realize prescribed apparent fracture toughness in thick-walled functionally graded material (FGM) circular pipes. The incompatible eigenstrain induced in the pipes after cooling from the sintering temperature due to the nonhomogeneous coefficient of thermal expansion is taken into consideration. An approximation method of finding stress intensity factors for a crack in the FGM pipes is introduced in which the nonhomogeneous material properties are simulated by a distribution of equivalent eigenstrain. A radial edge crack emanating from the inner surface of the homogenized pipes is considered for the case of a uniform internal pressure applied to the surfaces of the pipes and the crack. The stress intensity factors determined for the crack in the homogenized pipes represent the approximate values of the stress intensity factors for the same crack in the FGM pipes, and are used in the inverse problem of evaluating optimum material distributions intending to realize prescribed apparent fracture toughness in the FGM pipes. Numerical results obtained for a thick-walled TiC/Al 2 O 3 FGM pipe reveal that the apparent fracture toughness significantly depends on the material distributions, and can be controlled within possible limits by choosing an optimum material distribution profile.

Displacement potential approach to the solution of stiffened orthotropic composite panels under uniaxial tensile load

Abstract The current paper presents an analytical method for the analysis of elastic field in a stiffened unidirectional orthotropic composite panel under uniaxial tensile load in the direction of fibres. The mixed boundary value elasticity problem is formulated in terms of a single potential function ψ, expressed in terms of the displacement components. This function satisfies one of the differential equations of equilibrium automatically. Therefore, the mixed boundary value problem is reduced to the solution of a single differential equation of equilibrium along with the associated boundary conditions. The analytical solution is obtained in the form of an infinite series. Some numerical results of different stress and displacement components at different sections of the panel are presented in the form of graphs. The reliability and soundness of the method are verified by comparing the results with finite-difference and finite-element solutions of the problem. Good agreement of the results establishes the superiority of the present analytical method based on the displacement potential function.

Analysis of the Effect of Fiber Orientation on the Elastic Field in a Stiffened Orthotropic Panel under Uniform Tension using Displacement Potential Approach

The effect of fiber orientation on the stresses and displacements at different sections of a stiffened panel of orthotropic composite material under a uniform tension is analyzed. The supporting edge of the panel is rigidly fixed and two opposing edges are stiffened. The mixed boundary value plane stress elasticity problem is formulated in terms of a single displacement potential function ψ, defined in terms of the two displacement components. The solution of the problem is obtained in terms of the Fourier infinite series for two different fiber orientations of the orthotropic panel. Analysis of the results shows that the fiber orientation has significant effect on the distribution of stress and displacement components at different sections of the panel.

Displacement Potential Based Finite Difference Solution to Elastic Field in a Cantilever Beam of Orthotropic Composite.

This paper concerns the finite difference solution to the elastic field in a cantilever beam of unidirectional orthotropic composite material. The mixed boundary value plane elastic problem is formulated in terms of a single displacement potential function. The numerical scheme developed is demonstrated for a particular case of a boron/epoxy cantilever beam for two different loading conditions. Numerical results of different stress and displacement components at different sections of the beam are presented in the form of graphs. With a view to verifying the finite difference results, solutions are also obtained by finite element method. The comparison of the results ensures that the present displacement potential based finite difference scheme is relatively simple, reliable, and accurate enough to analyze the elastic field in orthotropic composite structures under mixed boundary conditions.

Analysis of Thermoelastic Characteristics of a Rotating FGM Circular Disk by Finite Element Method

This study concerns the analysis of thermoelastic characteristics of a thin circular functionally graded material (FGM) rotating disk having a concentric hole and subjected to a thermal load. The Youngs modulus, coefficient of thermal expansion (CTE), and density of the disk are assumed to vary exponentially in the radial direction only while the Poissons ratio is assumed to be constant. The incompatible eigenstrain developed in the FGM disk due to nonuniform coefficient of thermal expansion and change in temperature is taken into account. Based on the two-dimensional thermoelastic theories, the axisymmetric problem is reduced to the solution of a second-order ordinary differential equation. Using the variational approach and Ritz method, a finite element model is developed for numerical solution of the problem. The model is verified for a homogeneous circular rotating disk and demonstrated for an Al2O3/Al FGM disk. Some numerical results of thermoelastic field in the Al2O3/Al FGM disk are presented and discussed. It is found that the thermoelastic characteristics of an FGM disk are largely dependent on temperature distribution profile, radial thickness of the disk, angular speed of the disk, and the inner and outer surface temperature difference, and can be controlled by controlling these parameters.

Low Velocity Impact Behavior of Aluminum Honeycomb Structures

Impact behaviors of aluminum honeycomb sandwich panels (AHSPs) are investigated experimentally by using a drop weight test setup. The specimens of 12.7 mm cell size were tested by impacting at four different initial contact points, namely face center, corner, long edge and short edge of core cells, with two impactors of weights 5.25 kg and 11.9 kg, respectively. Dynamic nonlinear transient analysis was also carried out by a finite element simulation model developed based on continuum damage mechanics to account for nonlinear and elastoplastic behavior. The results revealed that while the impact behaviors of AHSPs were nearly the same for low impact energy, they were different for high impact energy. The peak resistance force of AHSPs was the highest for impact at the face center and the lowest for impact at the short edge of the core cells. The results of FE simulation revealed that the real time deformation produced fracture when the crack initiated and propagated to the honeycomb core from the facesheet.

Lyocell Fiber Reinforced Polypropylene Composites: Effect of Matrix Modification

Composites with polypropylene (PP) and lyocell fibers were manufactured by compression molding technique. In order to improve the interfacial adhesion between the natural fibers and thermoplastic matrix during manufacturing, maleic anhydride grafted polypropylene (MAPP) as a coupling agent has been employed. Physical properties such as void contents and water absorption rate were studied. Tensile and flexural tests were carried out to evaluate the composite mechanical properties. Tensile test results showed the higher strength and modulus of composite than pure polypropylene (PP). In addition, strength and modulus were found to be influenced by the variation of MAPP contents (1%, 2%). Unlike tensile properties, flexural properties were not improved. However, between 1 and 2 wt% MAPP content, the composites containing 2 wt % MAPP showed better flexural properties than 1 wt % MAPP.

A Mathematical Analysis of Thermoelastic Characteristics of a Rotating Circular Disk with an FGM Coating at the Outer Surface

A thin circular rotating disk having a concentric hole and a functionally graded material (FGM) coating at the outer surface is considered with a view to analyzing the thermoelastic characteristics due to a thermal load and rotation of the disk. The FGM coating is assumed to have exponentially varying Youngs modulus, coefficient of thermal expansion (CTE), and density in the radial direction of the disk. The Poissons ratio is assumed to be constant throughout the disk. The incompatible eigenstrain developed in the disk owing to the nonuniform CTE and variation of temperature is taken into consideration. Using the two-dimensional thermoelastic theories, the two-dimensional plane stress axisymmetric problem is formulated as a second order differential equation. A finite element model is developed using the variational approach and Ritz method to obtain the numerical solution of the differential equation. The validity of the finite element model is justified for a rotating circular disk of homogeneous material by comparing the finite element results with analytical solution obtained by Timoshenko. Then the finite element model is applied to the problem of an Al disk with an Al2O3/Al FGM coating at its outer surface. The numerical results of the thermoelastic field demonstrate that the temperature distribution profile, angular speed of the disk, and FGM coating thickness are the crucial factors to be considered in controlling the thermoelastic characteristics of a rotating disk with an FGM coating.