Assumed Stress Quasi-conforming Formulation For Research Of Composite Grid Stiffened Plates

Composite materials have many advantages such as high strength rate,high modulus rate,lighter weight,corrosion resistance,fatigue resistance,easy molding,etc.,and have been widely used in the automotive industry.As a kind of advanced structural form,composite grid-stiffened structure has the advantages of high structural design,environmental robustness and low manufacturing cost,at the same time,its quality is lighter than traditional laminate structure,which also has broad application prospects in the automotive field.Therefore,the need to establish a model for numerical analysis of the grid-stiffened structure is growing.Among the many analytical models,Smeared Stiffener Method has higher precision and efficiency,and is one of the best choices for periodic grid-stiffened structure analysis.The quasi-conforming finite element method is a very flexible and effective theoretical framework.The basic idea is to integrate the strain-displacement equation and the equilibrium equation together in the unit.The proposed finite element technique is widely used in plate and shell analysis because of its simplicity and high efficiency.In this paper,a static analysis of composite grid-stiffened panels is carried out under the framework of assumed stress quasi-conforming technique.The main work includes:Applying the First-Order Shear Deformation Theory(FSDT)and the Smeared Stiffener Method(SSM),this paper presents a four-node quadrilateral QC element in the framework of assumed stress quasi-conforming method for the composite grid-stiffened plates.An appropriate initial stress approximation ruled by 24 parameters are chosen to weaken the strain-displacement equations.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.So as to demonstrate the accuracy,validity,and applicability of the proposed four-node quadrilateral QC element for linear static bending of grid-stiffened plates,several numerical examples with different rib geometries,aspect ratios,loading cases,boundary conditions,skin lay up are investigated in this section.Numerical results have proved that the new element is free form shear locking,and possesses high accuracy for the analysis of the grid-stiffened plates.