Nonlinear finite element analysis for design of plated structures

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Nonlinear finite element analysis for design of plated structures


Author: Liu, Yaopeng
Title: Nonlinear finite element analysis for design of plated structures
Degree: Ph.D.
Year: 2009
Subject: Hong Kong Polytechnic University -- Dissertations.
Building, Iron and steel -- Design and construction.
Finite element method.
Structural analysis (Engineering)
Department: Dept. of Civil and Structural Engineering
Pages: xxiii, 280 leaves : ill. ; 30 cm.
Language: English
InnoPac Record:
Abstract: This thesis discusses the findings of a research project on analysis and design of bare and wall-framed steel structures. Extensive numerical examples have been employed to verify the proposed theory. The thesis further proposes an efficient and reliable computational tool for routine and advanced design of structures of steel material. It is common to note that many structural failures and collapses are due to structural instability which is more difficult and complex to consider than material yielding in the design context. For columns and bracings under large axial forces flexural buckling would tend to occur, whereas beams subjected to bending moments about their major axes may have lateral-torsional buckling. Meanwhile, the initial imperfections, including the global frame imperfection and the local member imperfection, should always be taken into account. In the first aspect, the consideration of initial imperfections transforms idealized bifurcation buckling to realistic load-deflection type buckling. On the other hand, the inclusion of initial member curvature is mandatory in modern design codes such as Eurocode-3 (2005) and BS5950 (2000) either in implicit (via use of different buckling curves) or explicit (via element formulation) consideration. Apart from the foregoing problems in practical engineering design, the contribution of structural walls and floor slabs are also commonly ignored in most previous second-order analysis. Thus, the applications of previous research are limited to bare steel frames. This cannot keep pace with the development and requirement in design of modern structures in which uses of structural plate elements are unavoidable. Furthermore, both researchers and engineers have been increasingly aware of the severe damage due to earthquake, especially after the impact of the Wenchuan Earthquake (2008) in China, and therefore there is a need to refine or improve the current seismic design methods with allowance for imperfections and wall and slab elements. In view of the above observations, there is an urgent need to develop a computational tool for stability analysis allowing for initial imperfections. Also, the common structural elements such as beams, columns, shear walls and floor slabs can be taken into consideration. In this thesis, a curved stability function element is formulated for nonlinear second-order analysis and design of steel frames. The proposed second-order analysis takes both the P-A and P-8 effects as well as the initial imperfections into account and as a result the traditional tedious member design can be replaced by the simple section capacity check. The proposed method is a system-based approach rather than a member-based method and therefore the true behavior of the structures can be reflected. Further, a flat shell element superimposed by a membrane element and a Mindlin type plate bending element is proposed for modeling and analysis of plated skeletal structures. The membrane part of the proposed shell element possesses the drilling degree of freedom and is free from 'zero-energy mode'. The bending part of the proposed shell element is based on the Reissner-Mindlin plate theory and the Timoshenko's beam theory. The convergence for the very thin plate is theoretically ensured and the 'shear locking' phenomenon is avoided. By introducing a simple geometric stiffness matrix, this shell element shows high performance and accuracy in tracing the post-buckling path both for 'snap-through' and 'snap-back' problems. To account for the lateral-torsional buckling, an integrated elastic buckling analysis by shell finite element and empirical equation as per the modified Perry-Robertson formulae is proposed to predict the design lateral-torsional buckling moment of beams. The drawbacks of the complicated large deflection and elasto-plastic shell finite element analysis which include uncertainty in modeling of residual stress and initial imperfection and excessively long computer time are overcome by the proposed method. The results by the present theory compare well with the closed form solutions and the one-dimensional beam element for simple cases. Using the proposed semi-empirical method, buckling resistance of beams with complex boundary conditions, geometries, loading types such as castellation in beams, loads above the shear centre and restraints at top flange have been effectively determined. To capture both the in-plane and out-of-plane behavior of structural walls, a shell element model is proposed for second-order analysis and design of wall-framed structures. Also, a simple floor element is suggested for consideration of the floor slabs while the imperfect stability function element is employed for modeling beam-column elements. Hence, the main structural elements of a typical building structure can be modeled in a nonlinear analysis and design and as a result the proposed second-order analysis method can be extended to typical composite building structures and not limited to the bare steel frames. In response to severe damage due to earthquake, a practical application by extending the proposed second-order analysis method for performance-based seismic design based on the pushover analysis procedure is developed. A simple and effective plastic hinge method is proposed here for inelastic pushover analysis. Meanwhile, the traditional nonlinear incremental-iterative procedure for proportional loads is modified to allow for non-proportional loads for simulation of pushover analysis which is carried out under constant gravitational loads with monotonically increasing lateral loads. Feature contained in this study is that it includes both the P-A and P-8 effects and their initial imperfections in global frame and local member levels which have not been mentioned in previous research. Moreover, the contribution of shear walls is considered by the proposed shell element. Therefore, a comprehensive method considering important effects is proposed for the performance based seismic design which can also be conducted using one element per member, being consistent with its counterpart for static load which is based on the one element per member model. This simplified modeling reduces the data manipulation effort and required computer time.

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