An exact solution for the statics and dynamics of laminated thick plates with orthotropic layers

An efficient meshfree method for vibration analysis of laminated composite plates

“…Analytical approaches have been also developed for composite laminates, for instance, Jiarang et al [32], Srinivas et al [33,34] and Vel et al [35] proposed exact solutions for static bending, vibration and buckling analysis of thick orthotropic plates and laminates, whereas sandwich plates and bidirectional composites have been examined by Pagono [36]. Furthermore, Leissa et al [37] successfully presented exact solutions for vibration and buckling analysis of a SS-C-SS-C rectangular plate loaded by linearly varying in-plane stress, and later Kang et al [38] further extended that method to study the free vibration problem of laminated composites subjected to in-plane moments acting on two opposite simply supported edges.…”

A state space augmented generalised RKPM for three-dimensional analysis of thick and laminated composite plates

“…A benchmark three-ply laminated plate problem [28,30,31,51] is then considered and the results obtained are compared with available analytical and numerical solutions. In the third example, a thick circular plate is modelled and the accuracy of the results is verified with those obtained from exact solutions and those generated by ABAQUS.…”

“…To validate the proposed method, the benchmark problem of a simply supported three-layer square plate loaded only on the top surface by a uniform normal pressure P 0 [28,31,51] is solved using the state space RKPM. The laminated plate consists of two identical face layers and a core layer, denoted as F 1 ; F 2 , and C. For each layer, the orthotropic material properties corresponding to Aragonite crystals are assumed as:…”

“…Using the fundamental equations of three-dimensional elasticity, Jiarang and Jianqiao [35] developed a formalism of the state equation for a general orthotropic body and presented a solution for a simply supported thick plate of arbitrary thickness. In a further development of this approach, they established the three-dimensional state equation for a simply supported thick orthotropic laminated plate and presented exact solutions for such structures [31]. Although such exact solutions are of particular importance because they provide benchmark solutions to validate various methods, these solutions are only applicable for simple cases and recourse to numerical approaches is needed for cases with complicated geometry and complex boundary conditions.…”

“…Clearly, developing a 3D method of analysis with lower computational cost attracts intense interest due to its suitability for the analysis of laminated composite plates. Of the most prevalent methods is the state space approach, which has been applied extensively for the analysis of laminated plates and shells [26,[28][29][30][31]. The most noticeable feature of the state space approach is that the size of the final system of equations is always independent of the number layers.…”