Static Analysis of Metallic and Composite Structures Using a Coupled Field Formulation

Abstract

In this thesis, specifically, for 1D problems, the variationally consistent methodology for newlinegenerating SSP models of 1D composite beams is evolved systematically and used to establish newlinesuch models corresponding to different composite higher-order beam theories. Numerical results newlineof isotropic, orthotropic, and generally laminated beams under transverse loading using four newlinewarping functions of the higher-order normal and shear deformation theories for different newlineboundary conditions are provided and compared with previous studies from the literature. newlineAlso, the exact static solutions of shear flexible thin-walled laminated open section beam of any newlinecross-section are derived using a unified coupled field formulation even in the presence of arbitrary newline newlinelamination sequence leading to coupling of extension, bending, shear and torsion terms in newlineconstitutive matrix. The formulation incorporates all non-classical effects like secondary warping, newlinewarping shear, transverse shear deformation, and constrained warping. This can potentially help newlinein extracting accurate cross-sectional stiffness which can be used in FE modeling of 1D thin-walled newlinecomposite (TWC) beams. Seven GE involving eight generalized forces and one compatibility newlinecondition are used to develop a 2 x2 SSP equation whose field variables are St Venant Torque (Mt) newlineand Bi-Moment (Mand#61559;). Their solution helps to derive explicit closed-form expressions for newlinedisplacements in terms of six generalized forces and eight rigid body displacements thus lending newlineitself amenable to develop an exact 2-node 7 degree of freedom (DOF) per node exact locking free newlineFE capable of satisfying both the natural and the essential boundary conditions (EBC). The exact newlineFE shall include both exponential and polynomial terms that help to capture the torsional response newlineaccurately. Also, the present formulation is shown to recover the well-known Vlasov solution for newlineisotropic thin-walled beams for different boundary conditions and inclusion of warping shear and newlinerelation between displacement and forces leads to efficient FE modeling of TWC beams. Examples newlineof isotropic beams subjected to distributed torsion and composite Channel, and I-beams subjected newlineto bending and torsion loads are studied in detail and compared favorably with available results. newlineFor the 2D Problems, the CFF is used to develop an efficient 4-node membrane element tolerant newlineand insensitive to mesh distortion by kinematically coupling the in-plane displacements which newlinesatisfy the equilibrium equations (EE) in Cartesian coordinates. This results in material-dependent newlinecoupled field interpolation functions making the element free from both volumetric and shear newlinelocking. The developed formulation provides a preliminary concept for the satisfaction of natural newlineboundary conditions (NBC) which is used to satisfy the strong patch test. Also, the present element newlinecan model a soft membrane-like rubber typically characterized by a Poisson ratio (and#61550;) approaching newline0.5 which the conventional displacement method fails due to volumetric locking. The proposed newlineelement was also demonstrated to provide superior results to the stress concentration problem and newlineassessed successfully for stress prediction in the neighborhood of a singular point by solving newlineFlamant s problem of a concentrated force at a point in a semi-infinite plate by comparing with newlineelasticity solutions. The proposed element also passed several benchmark problems from the newlineliterature, passed the weak patch test and the inf-sup test for both compressible and incompressible newlinecases. newline