Title:

The response of nonlinear structures by the pseudoforce influence method

For any nonlinearly responding body, an equivalent linearelastic model can be developed in which the material nonlinearity and inertial effects are represented as supplementary pseudoforces which act in addition to the physical loading. The pseudoforces can be decomposed into constant loadsets multiplied by (deformationdependent or displacementdependent) scaling factors. If the scaling factors can be determined, the overall nonlinear response can be found from the linearelastic model using the principle of superposition. For the class of problem in which the material nonlinearity is present in only localised regions, a reduced system of nonlinear equations whose unknowns are the scaling factors may be derived using an influence matrix technique. This 'reduction procedure', which we refer to as the PseudoForce Influence Method (PFIMethod), is the topic of this thesis. This dissertation is split into three parts. The contents of each are now briefly summarised. Part I (chapter 1) The pseudoforce concept and objectives of this thesis In Part I, we explain why nonlinear assessments of offshore structures may be required and discuss why general purpose finite element programs are not always suitable for such studies. The pseudoforce concept is introduced and proposed as an alternative approach that can provide the nonlinear response using linearelastic software. A historical review of the development of pseudoforce and related methods reveals that these methods have been used primarily to determine the response of modified linearelastic structures, and that the heuristic approach adopted by several researchers is not readily extended to complex nonlinear problems. Our primary objective is to develop, using pseudoforce principles, an efficient nonlinear analysis tool for the assessment of offshore braced frames. A secondary objective is to develop the pseudoforce formulation within a continuum mechanics framework to demonstrate formally that the PFIMethod is simply a reformulation of the displacementbased stiffness method that is often employed in conventional finite element packages. Part II (chapters 2 to 5) The PFIMethod for braced frames In Part II, we consider offshore braced frame structures, and in particular their nonlinear response when exposed to severe storms. Before advancing the theory of the PFIMethod for such structures, we begin in chapter 2 by addressing the following: governing failure modes of braced frames; construction of representative nonlinear structural models; procedures for static, cyclic and dynamic analyses, and criteria with which to judge the structure's adequacy. Consideration of the failure modes of offshore braced frames leads to the conclusion that the axial capacity of a few members governs the overall strength and that the bracing configuration plays a key role in the ability of the structure to redistribute load from buckling members. Some important aspects of nonlinear structural modelling are addressed with emphasis on how to model the axial capacity of the members using nonlinear bar elements. A member model based on plastic hinge theory is developed and a hysteretic algorithm for axial member capacity is described. Part III (chapters 6 and 7) A more formal treatment of the PFIMethod In chapter 6, continuum mechanics principles and plasticity theory are employed to provide a framework for the more general treatment of the PFIMethod which is developed in chapter 7. The resistance of a finite element is derived within a corotational reference system which is suited to large rotation, small strain, computations. The element resistance is developed in terms of its deformation modes. Only later are rigid body modes considered. Symbolic notation is used which enables the geometrically nonlinear stiffness matrices to be expressed explicitly in terms of the geometrically linear matrices. In chapter 7, a general theory for the PFIMethod is derived using the corotational approach developed in chapter 6. The symbolic notation adopted in chapter 6 allows the influence matrices to be formally defined and symmetries to be identified. Moreover, for geometrically linear problems, the equivalence of other related techniques such as the initial strain method also become apparent with this notation. Both nodal and element PFIMethods are developed, the distinction reflecting whether or not the pseudoforces are summed at common nodes. The number of pseudoforces required to represent material nonlinearity is shown to equal the number of deformation modes in the element. A procedure for incorporating global geometric nonlinearity without diminishing the overall effectiveness of the PFIMethod is discussed. Finally, the efficiency of the PFIMethod is compared to that of a conventional solution procedure operating on the global system matrix.
