3D Numerical Analysis of Cracked Ti-TiB FGM Plate with a Semicircular Notch Subjected to Different Modes Load Conditions

This study has been made to determine the performance of the (Ti-TiB) FGM plate to reduce the J-integral calculated for the crack tip emanating from the semicircular notch root in mode I and mixed mode, when the crack is propagated from the notch root. In this paper, 3D finite element method is applied to analyze the behavior of a crack emanating from semicircular notch root growing from the metal (Ti) and is oriented perpendicularly in direction of ceramic (TiB). The J-integral has been found for several combinations laws of FGM plates with respect to the variable combination of the crack length, the plate thickness, the notch radius, Young modulus of FGM plate constituents and the crack orientation. These parameters must be optimized in order to improve the best performances

Mechanical Stability Investigation of Advanced Composite Plates Resting on Elastic Foundations Using a New Four-Unknown Refined Theory

A refined and simple shear deformation theory for mechanical buckling of composite plate resting on two-parameter Pasternak’s foundations is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces.Therefore, there is no need to use shear correction factor. The number of independent unknowns of present theory is four, as against five in other shear deformation theories.It is assumed that the warping of the cross sections generated by transverse shear is presented by a hyperbolic function. The stability equations are determined using the present theory and based on the existence of material symmetry with respect to the median plane.The nonlinear strain-displacement of Von Karman relations are also taken into consideration. .The boundary conditions for the plate are assumed to be simply supported in all edges. Closed-form solutions are presented to calculate the critical load of mecanical buckling, which are useful for engineers in design. The effects of the foundation parameters,side-to-thickness ratio and modulus ratio, the isotropic and orthotropic square plates are considered in this analysis.are presented comprehensively for the mechanical buckling of rectangular composite plates

Mechanical stability investigation of advanced composite plates resting on elastic foundations using a new four-unknown refined theory

A refined and simple shear deformation theory for mechanical buckling of composite plate resting on two-parameter Pasternak钒s foundations is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces.Therefore, there is no need to use shear correction factor. The number of independent unknowns of present theory is four, as against five in other shear deformation theories.It is assumed that the warping of the cross sections generated by transverse shear is presented by a hyperbolic function. The stability equations are determined using the present theory and based on the existence of material symmetry with respect to the median plane.The nonlinear strain-displacement of Von Karman relations are also taken into consideration. The boundary conditions for the plate are assumed to be simply supported in all edges. Closed-form solutions are presented to calculate the critical load of mechanical buckling, which are useful for engineers in design. The effects of the foundation parameters, side-to-thickness ratio and modulus ratio, the isotropic and orthotropic square plates are presented comprehensively for the mechanical buckling of rectangular composite plate

Finite Element Analysis of Interactions of between two cracks in FGM notched Plate under Mechanical Loading

The investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. This paper introduces a numerical investigation used to calculate the J-integral of the main crack behaviour emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) FGM plate subjected to tensile mechanical load. Young’s modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-FGM) with exponential-law (E-FGM) function. Further, the Poisson’s ratio is taken as a constant in normal direction.  For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software.  The variation of the J-integral according to the position, the length, and the angle of rotation of cracks is demonstrated. The variation of the J-integral according to the position, the length, and the angle of rotation of cracks are examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce J-integral. According to the numerical analysis, all parameters above played an important role in determining the J-integral

Finite Element Analysis of Interactions between two cracks in FGM notched Plate under Mechanical Loading

The investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. This paper introduces a 2D numerical investigation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in titanium /titanium boride functionally graded material (TiB/Ti FGM) plate subjected to tensile mechanical load. Youngs modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-FGM) with exponential-law (E-FGM) function. Further, the Poisson蒒s ratio is taken as a constant in normal direction. For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length, and the angle of rotation of cracks are examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce J-integral. According to the numerical analysis, all parameters above played an important role in determining the J-integral

Multi-objective optimisation of the electric wheelchair ride comfort and road holding based on jourdain’s principle model and genetic algorithm

The paper addresses the multi-body modelling of an electric wheelchair using Jourdain’s principle. First, a description of the adopted approach was presented. Next, the mathematical equations were developed to obtain the dynamic behaviour of the concerned system. The numerical computation was performed with MATLAB (matrix laboratory: a high performance language of technical computing) and validated by MBD (Multi-Body Dynamics) for Ansys, a professional multi-body dynamics simulation software powered by RecurDyn. Afterwards, the model was treated as an objective function included in genetic algorithm. The goal was to improve the ride quality and the road holding as well as the suspension workspace. The multi-objective optimisation aimed to reduce the Root-Mean-Square (RMS) of the seat’s vertical acceleration, the wheels load and the workspace modulus by varying the bodies’ masses, the spring-damper coefficients and the characteristics of the tires. Acceptable solutions were captured on the Pareto fronts, in contrast to the relatively considerable processing time involved in the use of a random road profile generated by the power spectral density (PSD). During the process, the compatibility and the efficiency of Jourdain’s equations were inspected