Assumed Stress Quasi-conforming Formulation For Mechanical Analysis Of Laminated Plates

Because of many superior characteristics,such as higher strength rate,higher modulus rate,higher abrasion resistance,much lighter in weight,easy to mould and et.al,composite materials has become predominant in many engineering fields,especially in automobile fields with the rapid development of composite materials and the reduction of raw material prices.This has led to a growing demand for accurate numerical analysis of composite laminates.Meanwhile,increased use of composite laminated plates necessitates the development of precise theoretical model to accurately predict the behavior of the structures.First-order shear deformation theory(FSDT)is widely used to predict the response of layered structures for its less computational cost and ease of implementation.The quasi-conforming(QC)technique is a very flexible and efficient theory framework,and its basic idea is the weakening of strain-displacement equations in the element together with that of the equilibrium equations.The QC technique has been widely used in the analysis of plate and shell because of its advantages such as simplicity and high efficiency.In this paper,under the assumed stress quasi-conforming formulation,the mechanical analysis of composite laminates is performed.The following are the detailed topics studied in this dissertation:Firstly,this paper presents a novel formulation in the framework of assumed stress quasiconforming method for the analysis of anisotropic laminated plates and constructs a fournode quadrilateral QC element.First an initial stress approximation ruled by 24 parameters which satisfies the equilibrium equations is derived in order to improve the performance of the constructed element.Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations.Finally,the linear function and the Timoshenko’s laminated composite beam functions are adopted as boundary string-net functions of the membrane and the bending for strain integration,respectively.Next,so as to demonstrate the accuracy,validity,and applicability of the proposed fournode quadrilateral QC element for linear static bending and free vibration analysis of laminated plates,several numerical examples with different geometries,aspect ratios,length-to-width ratios,lay up,loading cases and boundary conditions are investigated in this section.The results obtained by present 4-node quadrilateral QC element are verified by comparing with other numerical and analytical solutions available in the literatures.Numerical results have proved that the new element is free from shear locking,and possesses high accuracy for the analysis of laminated plates.