The Response of Non-Linear Structures by the Pseudo-Force Influence Method

Stewart, Graham (1995) The Response of Non-Linear Structures by the Pseudo-Force Influence Method. PhD thesis, University of Glasgow.

Abstract

For any non-linearly responding body, an equivalent linear-elastic model can be developed in which the material non-linearity and inertial effects are represented as supplementary pseudo-forces which act in addition to the physical loading. The pseudo-forces can be decomposed into constant load-sets multiplied by (deformation-dependent or displacement-dependent) scaling factors. If the scaling factors can be determined, the overall non-linear response can be found from the linear-elastic model using the principle of superposition. For the class of problem in which the material non-linearity is present in only localised regions, a reduced system of non-linear equations whose unknowns are the scaling factors may be derived using an influence matrix technique. This 'reduction procedure', which we refer to as the Pseudo-Force Influence Method (PFI-Method), 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 pseudo-force concept and objectives of this thesis In Part I, we explain why non-linear assessments of offshore structures may be required and discuss why general purpose finite element programs are not always suitable for such studies. The pseudo-force concept is introduced and proposed as an alternative approach that can provide the non-linear response using linear-elastic software. A historical review of the development of pseudo-force and related methods reveals that these methods have been used primarily to determine the response of modified linear-elastic structures, and that the heuristic approach adopted by several researchers is not readily extended to complex non-linear problems. Our primary objective is to develop, using pseudo-force principles, an efficient non-linear analysis tool for the assessment of offshore braced frames. A secondary objective is to develop the pseudo-force formulation within a continuum mechanics framework to demonstrate formally that the PFI-Method is simply a reformulation of the displacement-based stiffness method that is often employed in conventional finite element packages. Part II (chapters 2 to 5) The PFI-Method for braced frames In Part II, we consider offshore braced frame structures, and in particular their non-linear response when exposed to severe storms. Before advancing the theory of the PFI-Method for such structures, we begin in chapter 2 by addressing the following: governing failure modes of braced frames; construction of representative non-linear 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 re-distribute load from buckling members. Some important aspects of non-linear structural modelling are addressed with emphasis on how to model the axial capacity of the members using non-linear 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 PFI-Method In chapter 6, continuum mechanics principles and plasticity theory are employed to provide a framework for the more general treatment of the PFI-Method which is developed in chapter 7. The resistance of a finite element is derived within a co-rotational 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 non-linear stiffness matrices to be expressed explicitly in terms of the geometrically linear matrices. In chapter 7, a general theory for the PFI-Method is derived using the co-rotational 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 PFI-Methods are developed, the distinction reflecting whether or not the pseudo-forces are summed at common nodes. The number of pseudo-forces required to represent material non-linearity is shown to equal the number of deformation modes in the element. A procedure for incorporating global geometric non-linearity without diminishing the overall effectiveness of the PFI-Method is discussed. Finally, the efficiency of the PFI-Method is compared to that of a conventional solution procedure operating on the global system matrix.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: Douglas Faulkner
• Keywords: Ocean engineering
• Date of Award: 1995
• Depositing User: Enlighten Team
• Unique ID: glathesis:1995-75738
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Dec 2019 09:15
• Last Modified: 19 Dec 2019 09:15
• URI: https://theses.gla.ac.uk/id/eprint/75738