| This dissertation is about a consistent smooth modeling of multidimensional nonlinear elastic and inelastic structural systems..;First, the One-Dimensional Smooth Hysteretic Model (1D SHM) and its various features, such as, a) basic hysteresis, b) kinematic hardening, c) strength and stiffness degradations, d) pinching, e) gap-closing, and f) asymmetric yielding are reformulated in time independent incremental form. The areas, in which the SHM needed further advancements, such as: a) nonlinear post-elastic spring, b) modified Gaussian pinching, c) alternative pinching model using tangent function, d) variable gap length, e) degradation of post-elastic stiffness, and f) embedding variation of strength in the expression of tangent stiffness are developed. With these additional features 1D SHM can emulate some of the complex nonlinear behaviors of structural members adequately.;Further, a modified version of 1D SHM is re-formulated to simulate the nonlinear elastic behavior. Spectra for nonlinear elastic and inelastic structures are developed, using the modified SHM and the parent SHM, respectively. These spectra are generated for various strength reductions, and inherent and supplemental damping. The difference between the two types of damping is explained both theoretically and numerically. The nonlinear elastic formulation can be applied to evaluate and design of "weakened structures" structures equipped with novel negative stiffness devices (NSD).;The final part of the dissertation expands the multi dimensional plasticity model to 3D space frame elements that include strength and stiffness deteriorations, large deformations and rotations, using flexibility based corotational formulation and incremental multi-axial theory of plasticity.;In the first phase of the above research, a new corotational formulation, based on flexibility modeling of space frames with large deformations and rotations, expanding prior developments, is done. The new expansion incorporates a) coupled axial, flexural and shear deformations, b) rigid rotations of chords with respect to the stationary global reference frame, c) formulation of geometric stiffness matrix by taking variations of the force equilibrium equation, d) re-derivation of the entire formulation in time-independent incremental form, and e) inclusion of improved numerical techniques within the corotational system. Using the modified formulation, several elastic large deformation-rotations and buckling problems of space frames, previously solved by various researchers through stiffness based approach, can be analyzed.;The second phase of the forgoing research involved: a) coupling between 3D geometric nonlinearity with large deformation and rotation, and multi-axial theory of plasticity, and b) incorporation of strength and stiffness deteriorations in the model. The resulting model combines the classical axial load-biaxial moment (P-M-M) interaction, coupled with geometric nonlinearity. Standard Newton method of iteration scheme is employed to generate the three dimensional hysteresis loops for stress resultants and deformational variables. For cases, where the structure experiences plastic buckling (i.e. when the determinant of the global tangent stiffness matrix approaches zero due to coupled material and geometric nonlinearity), the arc length method, with modifications done for cyclic loading analysis, is used to track the cyclic buckling and post-buckling equilibrium paths. Finally, hysteretic energy based strength degradation and deformational ductility based stiffness degradation are incorporated in the yield surface based on P-M-M interaction and the elastic stiffness matrix, respectively. Several benchmark examples for 3D beams are presented to illustrate the above developments. (Abstract shortened by UMI.). |
