Static analysis of stiffened laminated composite plates by using GDQM

Abstract

Due to their extensive use in the aerospace and maritime industries, stiffened laminated composite plates represent an important study topic in engineering. Due to their superior mechanical qualities and high strength-to-weight ratio, stiffened laminated composite plates are frequently employed in a variety of technical applications. This study examines the static analysis of an eccentric stiffener-equipped laminated composite plate. First-order shear deformation theory is used to mathematically model the main plate under investigation, which includes four layers of carbon/epoxy. In contrast, Timoshenko beam theory is used to describe the isotropic stiffener mathematically. A torsional coefficient is also employed and included in the mathematical beam model for isotropic stiffeners. Also, for modeling an isotropic plate, the Mindlin plate theory is used. The theoretical investigations seek to determine how the insertion of stiffeners impacts the lamination of composite plates' static behavior. The stiffened laminated composite plate's motion equations are derived in the theoretical analysis using Hamilton's principle. A numerical method known as the Generalized Differential Quadrature Method (GDQM) has demonstrated considerable promise in resolving challenging engineering issues. The GDQM approach, which discretizes the partial differential equations into a set of algebraic equations, is used in this study to solve the governing equation that represents the free vibration of eccentrically stiffened laminated composite plates. For each edge of the plate, the clamped boundary conditions are taken into account. The Wolfram Mathematica application is an effective suite of tools for numerical analysis and scientific computing. It is used for numerical problem-solving and result visualization. This study investigates the natural frequencies and mode shapes of an isotropic stiffened plate for isotropic plate, [0,90,90,0] and [45,60,60,45] fiber angle carbon fiber laminated composite. The findings demonstrate that the GDQM method is a reliable and accurate approach for determining the free vibrations of such plates. The results also show that changing the fiber angle orientation significantly affects the mode shapes and can vary the natural frequencies. These findings are applicable in a variety of engineering disciplines for the design and analysis of stiffened laminated composite plates.