Dynamic analysis of a stiffened composite plate

Composite materials which are developed as lighter and stronger materials for the aerospace industry in the 1960s have now become widespread and been used in many industries such as marine, construction and automotive. They provide a better alternative to old standby materials like aluminum, steel, wood and concrete. In particular composite materials combine high strength and low weight together, while at the same time they have high resistance to corrosive and thermal effects. They provide great weight savings because of the specific properties and low weight of the individual components which form the composite material. They also have high impact strength and design flexibility. Correspondingly they can be designed for a particular type of load. All these characteristics make composite materials indispensable for the aeronautical and aerospace structures. Composite materials that are used in aerospace structures are usually built up with laminates where unidirectional fabric layers are stacked on top of each other in different orientations to give the structure maximum stiffness where it is needed. Cutting edge technology aircrafts substantially comprise stiffened laminated composite plates in many parts. For laminated composite plates, orientation of fibers is the most important case that effects plates strength and rigidity. Focusing on this parameter for different boundary conditions results in lighter and stronger structures. In addition to that, there are other significant parameters for stiffened composite plates such as direction, shape and material. All these parameters should be considered together to obtain structures that have higher strength and lower weight. In this study, optimum fiber orientation for square and rectangular laminated plates and optimum shape, direction and material for stiffeners are examined. First, a general information about composite materials and plate equations is given. Then, some composite plates and stiffened composite plates samples are formed, and static and dynamic analyses are conducted to compare those plates, and finally better combinations are determined. ANSYS 16.2 ACP module is used for design procedure and analysis performed in ANSYS Workbench 16.2. Some analytical formulas available in literature are used for validation of analysis of bare plates. In this context, numerical analysis is performed for bare laminated composite plates and stiffened laminated composite plates. First, a square laminated composite plate with 8 epoxy-carbon unidirectional layers considered. Edge length of the square plate is chosen as 500 mm and thickness of the plate as 4 mm., Free vibration and static analysis under distributed load of plates are examined for different fiber orientations of layers under different boundary conditions. For all sides simple supported case, minimum deflection and maximum fundamental natural frequency occur at (45,-45)4 orientation. For all sides clamped case, minimum deflection and maximum fundamental natural frequency occur at (0,0)4 and (90,90)4 orientations. (45,-45)4 orientation yields lower stress levels for both cases. Free vibration analysis is also performed for different boundary condition combinations such as SSSS, CCCC, CSCS, CCSS, CCFC, SSCS, SSFS, SSFF and CCFF. Best angle orientations for each case are provided. Analyses that are performed for all side simple supported and all side clamped boundary conditions are repeated for rectangular plates by changing aspect ratio to 1/2, 1/3 and 1/4. Laminated rectangular plates with fibers along the short edge produce less deflection and higher fundamental natural frequency for both boundary conditions. However, higher natural frequencies increase for (45,-45)4 orientation. Second, a laminated composite plate is designed with dimensions Lx=500mm and Ly=1000mm. A comparison between bare plate and stiffened plate with the same weight is made and it is found that stiffeners reduce the deflections and stresses of plate but, increase natural frequencies significantly. The use of stiffener also changes mode shapes. In order to see the effect of the stiffener cross sectional shape, different profiles such as rectangular, I, T, inverse-T, L, inverse-L and Z shaped composite stiffeners with the same height and volume are designed by using the same type layers of the plate. Stiffeners are oriented along the y- direction and at the middle of the plate. Static analysis is conducted under 1 kPa distributed pressure on the top surface of the plate. Maximum deflection and stress are obtained under all side clamped boundary conditions. It is found that inverse-T shaped stiffener results in less deformation and stress levels. The order of maximum deflection and maximum stress levels for each stiffener is inverse-TL>I>Z>rectangular>T>inverse-L. For higher modes, it is found that natural frequencies don't change significantly. Harmonic response analysis of each sample is performed from 1 Hz to 1000 Hz under distributed 1 kPa pressure on the top surface of the plate. Frequency response of the plate is observed. It is seen that samples reach their peak values at their fundamental natural frequencies. The order of amplitude values at peak points is inverse-T