The use of laminated composites has been increasing day-by-day in various fields of engineering. Laminated composite plates are quite often subjected to dynamic loads and hence it is vital to study the dynamic behavior of such structures. Structural performance of these composite plates need to be evaluated properly, when they are subjected to dynamic loads. The behaviour of laminated composite plates are affected by excessive vibrations, higher displacements and accelerations which may severely deteriorate the structural performance, when they are subjected to dynamic loads such as impulsive loads. So, there is a need to find out a fiber orientation, that produces least dynamic response parameters. Hence, the purpose of this research work is to investigate the dynamic response of the laminated composite plates subjected to excitations, varying arbitrarily with time and to suggest a robust fiber orientation. Laminates may be provided with holes to cater for different purposes in various streams of engineering. Static, Modal and Transient dynamic analysis of laminated composite plates, simply supported at all the edges has been carried out in this study. Laminated composite plates with holes at different positions are investigated for different fiber orientations by considering two types of loadings i.e., Triangular impulsive loading and Rectangular impulsive loading. This part of the research has been carried out using finite element software ANSYS 13.0.
Laminated composites are used widely in various disciplines such as civil, aerospace, automobile, naval, industrial buildings etc., in the form of prefabricated plywood laminates. They became popular due to their lightweight and high strength. Laminated composites are a series of lamina or plies stacked together with different materials, ply thicknesses, and mechanical properties. Each lamina is stacked with various fibre orientations to obtain required directional stiffness and strength properties. Ply stacking sequence is very important to obtain an efficient lamina. Weight reduction, limitations of natural frequencies, displacements, and accelerations aim at structural improvement of cost, performance and reliability in the design of plates and shells.
Laminated composite plates are quite often subjected to dynamic loads. These dynamic loads are neither harmonic nor periodic. In this research work, laminated composite plates simply supported on all sides and subjected to static, free vibration and transient loads are analysed for thirteen fiber orientations (0/0/0/0/0, 0/30/45/30/0, 0/30/0/30/0, 0/45/0/45/0, 45/0/45/0/45, 45/0/0/0/45, 45/-45/0/-45/45, 30/60/90/60/30, 30/-45/0/- 45/30, 90/45/0/45/90, 90/-60/45/-60/90, 90/0/90/0/90, 0/90/0/90/0). Finite element modelling and analysis of laminated plates is carried out using ANSYS 13.0 software.
J. Chen, D.J. Dawe, and S. Wang (2000) developed the semi-analytical finite strip method for the analysis of the geometrically nonlinear response to dynamic loading of the rectangular composite laminated plates. The comparison has confirmed the validity of the new procedure which offers advantages of economy and efficiency in comparison with competing procedures.
Y.M. Desai, G.S. Ramtekkar, and A.H. Shah (2003) carried out the free vibration analysis of multi-layered thick composite plates using three-dimensional, higher order, mixed Finite Element (FE). Comparison of natural frequencies with elastic and various analytical/FE solutions revealed that the formulation is capable of dealing with the dynamic analysis of laminated composite plates.
Pathak, K.K., Vipin Arora and Jain J.K., (2007) studied the transient dynamic analysis of three dimensional composite laminated plates. Simply supported plates made up of five layers, two orthotropic materials stacked in alternate layers are investigated. Number of plates are analyzed by varying the fiber orientation, thickness and type of loading.
A. Houmat, (2012) investigated the geometrically nonlinear free vibration of a composite rectangular plate with variable fiber spacing and found that the hardening behavior of the plate with variable fiber spacing decreases with increasing fiber volume fraction. The simply supported plate presents a more accentuated hardening behavior than the clamped one.
Sharayu, U. Ratnaparkhi, and S.S. Sarnobat (2013) conducted experiments to investigate the free vibration response of the woven fiber Glass/Epoxy composite plates in free-free boundary conditions. It is found that the natural frequency decreases as the ply orientation increases up to [45/-45] and again increases up to [30/- 60].
Sang Jin Lee, and Ha Ryong Kim (2013) investigated structural behavior of laminated composite plates by developing a four-node laminated plate element using a Higher Order Shear Deformation Theory (HSDT). It is found that the proposed FE is very effective to remove the locking phenomenon and produces reliable numerical solutions for most laminated composite plate structures.
Bahi-Eddine Lahouel and Mohamed Guenfoud, (2013) carried out vibration analysis on symmetric angle-ply laminated composite plates with and without square holes when subjected to compressive loads. Buckling analysis is also performed to determine the buckling load of laminated plates. The results showed that the presence of a constant compressive load tends to reduce uniformly the natural frequencies for materials which have a low degree of orthotropy.
Junaid Kameran Ahmed, V.C. Agarwal, P. Pal, and Vikas Srivastav, (2013) carried out Static and Dynamic analysis of Graphite / Epoxy composite plates under transverse loading. The minimum deflection was found at an angle of 150 for clamped plates and in case of simply supported plates, the minimum deflection was found at an angle of 450.
Syed Altaf Hussain, V. Pandurangadu, and K. Palani Kumar (2014) carried out free vibration analysis of a four layered angle-ply symmetric laminated plates with various lamination angles (±0o to ±90o ) of laminas with different hole locations. It is found that the fundamental frequency of laminated composite plates decreases with increase in L/h ratio.
Suleyman Basturk, Haydar Uyanık, and Zafer Kazancı (2014) investigated the nonlinear dynamic response of a hybrid laminated composite plate composed of basalt, Kevlar/epoxy and E-glass/epoxy under the blast load with damping effects and found that the deflection amplitude and the vibration frequencies increase while increasing the peak pressure value.
A rectangular laminated composite plate 3m x 2m simply supported on all sides is analysed in this paper. The laminate consists of five layers and thickness of each layer is 4mm. Diameter of the hole is 0.5m. Finite element analysis of the plate is carried out using a layered shell element and is shown in Figures 1 to 4. The plate is discretized into 1204 elements and 1276 nodes. For static analysis, uniform pressure of 1000 N/m2 is applied on the plate. For transient dynamic analysis, two types of dynamic loads i.e., triangular impulsive load as shown in Figure 5 and rectangular impulsive load as shown in Figure 6 are applied on the plate. The peak load at each node is 10 N and load duration is one second in both the cases. Laminated composite plates subjected to static, modal, and transient dynamic loads are analysed for thirteen different fiber orientations as shown in Figures 7(a) and (b).
Figure 1. Finite Element Model of Simply Supported Plate without Hole
Figure 2. Finite Element Model of Simply Supported Plate with Central Hole
Figure 3. Finite Element Model of Simply Supported Plate with two Interior Holes
Figure 4. Finite Element Model of Simply Supported Plate with Four Corner Holes
Figure 5. Triangular Impulsive Load – Load Case 1
Figure 6. Rectangular Impulsive Load - Load Case 2
Figure 7(a). Fiber Orientation-1 is SS Laminated Composite Plate
Figure 7 (b). Fiber Orientations in SS Laminated Composite Plate
The laminate considered is made up of two orthotropic materials, stacked alternatively to make a full plate. First, third and fifth layers are made of material-1 and second and fourth layers are of material-2. The mechanical properties of materials are taken from K.Maithry and B.D.V Chandra Mohan Rao (2015) are given in Table1.
Table 1. Mechanical properties of Materials
A rectangular laminated composite plate simply supported along all the four edges is subjected to a uniform pressure of 1000 N/m2 . The maximum and minimum deflections for various fiber orientations are given in Table 2.
Table 2. Static Response of Simply Supported Laminated Composite Plate (Deflection in mm)
For a simply supported plate without hole, it is observed that the peak deflection is minimum in the case of 90/- 60/45/-60/90 and maximum in case of 0/0/0/0/0.
For the plate with central hole, it is observed that the peak deflection is minimum in the case of 90/45/0/45/90 and maximum in case of 0/0/0/0/0.
For the plate with two interior holes, it is observed that the peak deflection is minimum in the case of 45/-45/0/-45/45 and maximum in case of 0/0/0/0/0.
For the plate with four corner holes, it is observed that the peak deflection is minimum in the case of 0/90/0/90/0 and maximum in case of 90/-60/45/-60/90.
Free vibration analysis is carried out on a rectangular laminated composite plate simply supported along all the four edges. The maximum frequency obtained for various fiber orientations are given in Table 3.
Table 3. Modal Response of Simply Supported Laminated Composite Plate (Frequency in Hz)
For a simply supported plate without hole, it is observed that the frequency is minimum in the case of 0/0/0/0/0 and maximum in case of 90/-60/45/-60/90.
For the plate with central hole, it is observed that the frequency is minimum in the case of 0/0/0/0/0 and maximum in case of 45/-45/0/-45/45.
For the plate with two interior holes, it is observed that the frequency is minimum in the case of 0/0/0/0/0 and maximum in case of 45/-45/0/-45/45.
For the plate with four corner holes, it is observed that the frequency is minimum in the case of 90/-60/45/-60/90 and maximum in case of 0/90/0/90/0.
A rectangular laminated plate simply supported along all the four edges is subjected to a triangular impulsive load i.e. load case-1. The maximum response parameters i.e. Deflection, and Velocity are obtained for various fiber orientations given in Tables 4 to 7.
Table 4. Maximum responses of SS Laminated Plate – No Hole, Load Case 1
Table 5. Maximum responses of SS Laminated Plate - Central Hole, Load Case 1
Table 6. Maximum responses of SS Laminated Plate – 2 Interior Holes, Load Case 1
Table 7. Maximum responses of SS Laminated Plate - 4 Corner Holes - Load Case 1
For a simply supported plate without hole, it is observed that the peak deflection, velocity is minimum in the case of 90/-60/-45/60/90 and maximum in case of 0/0/0/0/0 and 0/90/0/90/0 respectively. Hence, 90/-60/-45/60/90 is the most robust orientation with respect to various response parameters.
For a simply supported plate with a central hole, it is observed that the peak deflection, velocity is minimum in the case of 90/45/0/45/90 and maximum in case of 0/0/0/0/0. Hence, 90/45/0/45/90 is the most robust orientation with respect to various response parameters.
For a simply supported plate with two interior holes, it is observed that the peak deflection, velocity is minimum in the case of 45/-45/0/-45/45 and 90/45/0/45/90 respectively and maximum in case of 0/0/0/0/0 and 30/60/90/60/30 respectively. Hence, 45/-45/0/-45/45 is the most robust orientation with respect to various response parameters.
For a simply supported plate with four corner holes, it is observed that the peak deflection, velocity is minimum in the case of 0/90/0/90/0 and 0/0/0/0/0 respectively and maximum in case of 90/-60/45/-60/90 and 0/45/0/45/0 respectively. Hence, 0/90/0/90/0 is the most robust orientation with respect to various response parameters.
A rectangular laminated plate simply supported along all the four edges is subjected to a rectangular impulsive load i.e. load case-2. The maximum response parameters i.e. Deflection, and Velocity are obtained for various fiber orientations given in Tables 8 to 11.
Table 8. Maximum responses of SS Laminated Plate – No Hole, Load Case 2
Table 9. Maximum responses of SS Laminated Plate – Central Hole, Load Case 2
Table 10. Maximum responses of SS Laminated Plate – 2 Interior Holes, Load Case 2
Table 11. Maximum responses of SS Laminated Plate – 4 corner holes, Load Case 2
For a simply supported plate without hole, it is observed that the peak deflection, velocity is minimum in the case of 90/-60/- 45/60/90 and maximum in case of 0/0/0/0/0 and 0/30/45/30/0 respectively. Hence, 90/-60/-45/60/90 is the most robust orientation with respect to various response parameters.
For a simply supported plate with a central hole, it is observed that the peak deflection, velocity is minimum in the case of 90/45/0/45/90 and 0/90/0//90/0 respectively and maximum in case of 0/0/0/0/0 and 0/30/0/30/0 respectively. Hence, 90/45/0/45/90 is the most robust orientation with respect to various response parameters.
For a simply supported plate with two interior holes, it is observed that the peak deflection, and velocity is minimum in the case of 45/-45/0/-45/45 and 45/0/0/0/45 respectively and maximum in case of 0/0/0/0/0. Hence, 45/-45/0/-45/45 is the most robust orientation with respect to various response parameters.
For a simply supported plate with four corner holes, it is observed that the peak deflection, and velocity is minimum in the case of 0/90/0/90/0 and 45/0/0/0/45 respectively and maximum in case of 90/-60/45/-60/90 and 0/30/0/30/0 respectively. Hence, 0/90/0/90/0 is the most robust orientation with respect to various response parameters.
The present work can be further extended as below.
E11 - Longitudinal Elasticity Modulus
E22 - Transverse Elasticity Modulus
E33 - Longitudinal Elasticity Modulus
μ12 - In-plane Poisson's ratio
μ23 - Transverse Poisson's ratio
μ31 - In-plane Poisson's ratio
G12 - In-plane Shear Modulus
G23 - Transverse Shear Modulus
G31 - In-plane Shear Modulus
F – 1- 0/0/0/0/0
F – 2- 0/30/45/30/0
F – 3- 0/30/0/30/0
F – 4- 45/0/45/0/45
F – 5- 45/0/0/0/45
F – 6- 45/-45/0/-45/45
F – 7- 30/60/90/60/30
F – 8- 30/-45/0/-45/30
F – 9- 90/45/0/45/90
F – 10- 90/-60/45/-60/90
F – 11- 90/0/90/0/90
F – 12- 0/90/0/90/0
F – 13- 0/45/0/45/0
