Nonlinear Computational Technology For Metallic And Composite Thin-walled Structures

The high strength alloy and composite thin-walled structures are widely used in aviation, aerospace, marine, automobile and other engineering structures, due to their high load carrying capability efficiency. The design of the thin-walled structures often needs to consider the geometrically nonlinear effects caused by the large displacement and large rotation. The nonlinear finite element analysis of the thin-walled structures not only can reduce the cost of prototypes testing and avoid blind experiments, but also can better understand the behavior of the structures under external loading to design a safer and more economical structure through shorter time. Although the development of nonlinear finite element analysis technology tends to be mature, the currently existing commercial finite element analysis software cannot fully meet the engineering requirements for simplicity, efficiency, accuracy in the analysis. Therefore, the research of the technology of the nonlinear finite element analysis for the thin walled structures is of important engineering practical value and academic significance.Thin-walled structures mainly take the form of beams, plates and shells and their combinations. At the limit load state, these structures are prone to undergo large displacement and large rotation, but the strains are often very small. Mostly the materials in the thin walled structures keep in the elastic region until buckling occurs, except that plastic deformation may occur for the thicker metal structures. Because the corotational formulation can easily expand the geometrically linear finite elements to geometrically analysis characterized by large deflection, large rotation but small strain, and the material nonlinear effects can be treated as the usual small deformation theory, the author develops a set of nonlinear finite element analysis program for metal and composite thin-walled structures based on the corotational formulation, and the main work are:1) The element-independent corotational formulations are deduced, making those elements which have the same node number and degrees of freedom can be extended to nonlinear analysis based on the same corotational formulation. Considering the non-additive characteristics of large rotating in3D space, the storage and update strategy of the rotation degrees of freedom which is valid for arbitrary large rotation are proposed for the beam elements and shell elements. The load control method, displacement control method and arc-length method are used to control the load step, making the developed nonlinear finite element formulations can be used to analyze the nonlinear post-buckling problems of the thin walled structure.2) Based on the first-order shear deformation theory, the unified formula of the generalized constitutive matrices for elastic material (including isotropic and laminate) and elastic-plastic material shell structures analysis are deduced. A more efficient formula for calculating the stiffness of the composite laminates is given, and the transverse shear stiffness can be directly calculated so that the shear correction factors are not needed again. The conventional Timoshenko beam function method (TBF) is improved to make it be efficient in development of thin-thick composite laminated shell elements. The Von-Mises yield criterion with isotropic hardening rule and the Prandtl-Reuss associated flow rule are used in the elasto-plastic analysis of the metallic thin-walled structures, and the explicit expression of Newton-Simpson integration formula along the thickness direction of the shell structures is deduced and it is suitable for the flat shell elements and solid-shell elements.3) Based on the improved TBF method, two new thin-thick triangular flat shell elements GTS3and OTS3, both having3nodes18degrees of freedom, are developed. Both of them can be used in the analysis of large deflection and nonlinear buckling analysis of the elastic and composite laminate shell structure, the element OTS3can also be used in the elastoplastic post-buckling analysis of the metal thin-walled structure.4) Based on the improved TBF method and the quadrilateral area coordinate method, two new thin-thick quadrilateral flat shell element QTS4θλ and QTS4, both having4nodes24degrees of freedom, both of them can be used in the analysis of large deflection and nonlinear buckling analysis of elastic and composite laminate shell structures, the element QTS4can also be used in the elastoplastic post-buckling analysis of the metal thin-walled structure.5) A new space Timoshenko beam element TM3, having2nodes and12degrees of freedom, is developed and it can be applied to beam structures with all kinds of section shape, and two different offset formula suitable for large rotation analysis are deduced and it is applicable to the large deflection and nonlinear buckling analysis of the stiffened plate/shell structures which are the combinations of the beams and shells.6) A new solid shell element SoidS8, which has8nodes and24degrees of freedom, has been developed. And it is applicable to the elastoplastic large deflection analysis and nonlinear buckling analysis of the metal thin-walled structure.A large number of numerical examples are given to validate the new developed nonlinear finite element formulations, and the performances of the present formulations are compared with those from literature and commercial software. The results show that the present beam elements, shell elements and solid element are accurate and efficient, and they can be combined for the nonlinear analysis of metal and composite thin-walled structure.