Higher-Order Non-Linear Analysis of Steel Structures Part Ii : Refined Plastic Hinge Formulation

Iu, Chi Kin; Bradford, M A

doi:10.18057/ijasc.2012.8.2.6

Cited by 7 publications

(7 citation statements)

References 25 publications

(34 reference statements)

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“…In regard to the element displacement and force solutions, Figures 8 and 9 display the deflection and bending moment distribution along a cantilever at a specific level 1.83 (load factor =0.56), which is indicated by dash line in Figure 7. Similarly, the element responses, such as deflection and bending moment as respectively shown in Figures 8 & 9, from the present method are consistent with the nodal solutions from those of Iu and Bradford [3] [4]. It is interesting to note that the rigid body motion is taken into account for P- effect, whereas the bending moment is directly generated from the natural deformation of an element, such as its curvature.…”

Section: A Cantilever Subjected To Uniform Element Load and Axial Comsupporting

confidence: 81%

“…In Figure 11, the element displacements (i.e. =1) from the present method are exactly same as the nodal displacements from the Iu and Bradford [3] [4]. However, at =2.7, the deflections of the columns of the frame emerge slight discrepancy with the nodal solutions from Iu and Bradford [3][4] as given in Figure 11, which can be attributed to the solutions near the numerical instability at divergence.…”

Section: A Simple Portal Sway Frame Subjected To Vertical Uniform Loamentioning

confidence: 51%

“…The popular displacement-based finite element approach was devoted by (hierarchic displacement element: mesh refinement required) a number of scholars; Meek and Tan [1], Chan and Kitipornchai [2] and Iu and Bradford [3] [4] among others and hence the conventional displacement-based finite element approach have been well established.…”

Section: Introductionmentioning

confidence: 99%

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Generalised Element Load Method With Whole Domain Accuracy for Reliable Structural Design

Iu¹

2016

Volume 12 Number 4

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This paper presents a formulation to capture all kinds of second-order effects (i.e. discrete nodal displacement as the numerical approach: P- & P- effect, large displacement, snap-through buckling, initial imperfection, etc.) for members under loads along their lengths. The efficient computational formulation of the generalised element load method (GELM) is proposed which gives accurate element and nodal solutions when using the one-element-per-member model. It is believed the GELM provides a reliable and efficient method for improving the second-order analysis for design of practical structures.Keywords: Generalised element load method; second-order elastic analysis; one element per member; higher-order element formulation; initial imperfection; element solutions DOI:10.18057/IJASC.2016.12.4.6 INTRODUCTIONNonlinear numerical analysis for a structure was prevalent from the past half century, likely because of availability of low-cost and powerful computers. In spite of its robustness, versatility and applicability, the conventional displacement-based finite element analysis possesses a drawback of element discretisation for a member to give accurate solutions when loads are along a member. To overcome the drawback, Chan and Zhou [5][6] presented a PEP finite element to simulate the second-order effect on a member with an initial geometric imperfection. Izzuddin [7] later formulated a fourth-order displacement-based finite element for structures under thermal loads. Iu and Bradford [8] provided a higher-order finite element analysis to examine various kinds of geometric nonlinearities for framed structures using a single element per member.Previous methods and their applications on second-order analysis for members under element loads are very limited to conversion of element loads to the nodal solutions and hence the major setback of these approaches is less accurate solutions obtained when using a single element to simulate a member with loads along its length. In order to take the element load effect into account for the member behaviour, Zhou and Chan [9, 10] presented a second-order elastic analysis that is capable of modelling the element load effect in the element stiffness formulation, in lieu of by a system analysis for the nodal solutions. Unfortunately, each element load case requires a specific element stiffness matrix, which is limited in practical applications because of the multiplicity of load patterns imposed on an element. And also no accurate solution along an element was evaluated in their research works.

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Section: A Cantilever Subjected To Uniform Element Load and Axial Comsupporting

confidence: 81%

Section: A Simple Portal Sway Frame Subjected To Vertical Uniform Loamentioning

confidence: 51%

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Generalised Element Load Method With Whole Domain Accuracy for Reliable Structural Design

Iu¹

2016

Volume 12 Number 4

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“…This paper uses a fourth-order displacement function [27,28] to simulate the member bowing behaviour; this necessitates the use of an additional equilibrium condition which constitutes a secondary or statical boundary condition, as illustrated in Fig. 1.…”

Section: Finite Element Formulationmentioning

confidence: 99%

Second-order elastic finite element analysis of steel structures using a single element per member

Bradford

2010

Engineering Structures

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a b s t r a c tFinite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies. Crown

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“…Izzuddin [4] subsequently formulated a fourth-order displacement-based finite element for structures under thermal loads, while Liew et al [5] made use of a stability function formulation in their stiffness matrices so that geometric non-linearity in a member could be incorporated. Recently, Iu and Bradford [6][7] [8] have developed the higher-order element using higher-order element, which showed the great applications of second-order inelastic framed structures.…”

Section: Introductionmentioning

confidence: 99%

Novel Non-Linear Elastic Structural Analysis With Generalised Transverse Element Loads Using a Refined Finite Element

Bradford²

2015

Volume 11 Number 2

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ABSTRACT:In the finite element modelling of structural frames, external loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. For a first-and second-order elastic analysis, the accurate displacement solutions of element load effect along an element can be simulated using neither lumping nor consistent load methods alone. It can be therefore regarded as a unique load method to account for the element load nonlinearly. In the second-order regime, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, this paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal solution (system analysis) to both nodal and element solution (sophisticated element formulation). For the conventional finite element method, such as cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within element, and as a result, it hinders the engineering applications.Keywords: Elastic instability, Finite element, Transverse element load effect, Higher-order element formulation, Nodal solution, Element solution INTRODUCTIONGeneral load cases for framed structures, such as permanent loads, live loads and wind loads, usually involve patterns of loading which act transversely along the elements of the frame. It is usual in the finite element modelling to convert these loads to nodal loads, and to discretise the member into several elements, with the transverse loads taken account of as nodal forces in order to capture the firs...

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Higher-Order Non-Linear Analysis of Steel Structures Part Ii : Refined Plastic Hinge Formulation

Cited by 7 publications

References 25 publications

Generalised Element Load Method With Whole Domain Accuracy for Reliable Structural Design

Generalised Element Load Method With Whole Domain Accuracy for Reliable Structural Design

Second-order elastic finite element analysis of steel structures using a single element per member

Novel Non-Linear Elastic Structural Analysis With Generalised Transverse Element Loads Using a Refined Finite Element

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