Generalised element load method for first- and second-order element solutions with element load effect

Iu, Chi Kin

doi:10.1016/j.engstruct.2015.03.016

Cited by 4 publications

(4 citation statements)

References 32 publications

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“…Hence, the external work done V constitutes two components; first component Vf (Lumping load method) is the work done by nodal loads fk in going through nodal displacements uk; second component V (Consistent load method) is the work done by transverse element load k in going through the assumed transverse displacement field associated with the element displacement function N over the element length. In accord with the assumption of conservative loads, the work done going through the deflected element N due to element loads is independent of the axial load q at all stages, such as setting q = 0 in the higher-order element function in [Iu [15]] [15], as given by…”

Section: Stiffness Formulation For Higher-order Element With Element mentioning

confidence: 93%

“…4 is identically carried out along the domain of an element, as the pattern of displacement function in [Iu [15] in the course of the system solution procedures as mentioned in Section 3. Therefore, the second-order solution due to a diverse kind of element loading can be unified by summing up the standardized and fundamental simple element load cases given in Appendix I of [Iu [15]].…”

Section: Stiffness Formulation For Higher-order Element With Element mentioning

confidence: 99%

“…in which u, v and w are dependent variables for axial deformation, for lateral deflections in the direction in y-axis and z-axis, respectively, which is given in [Iu [15]];  is for twist angle about x-axis; EA, EI and GJ are the axial rigidity, flexural rigidity about corresponding axes and torsional rigidity, respectively; P is the axial element load.…”

Section: Stiffness Formulation For Higher-order Element With Element mentioning

confidence: 99%

“…It means that a reliable structural analysis for members subjected to external element loads is unavailable with an error contained in analysis by one-element-per-member model for members with loads along the lengths. The lumping and consistent load methods alone are unable to produce accurate first-and second-order elastic solutions due to element load effect within an element itself as reported by Iu and Bradford [14] and Iu [15]. In this paper, a qualified element for these purposes is proposed and it transforms the traditional discretised nodal solution into continuous displacement and force element solutions for the geometric nonlinear effects.…”

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: Stiffness Formulation For Higher-order Element With Element mentioning

confidence: 93%

Section: Stiffness Formulation For Higher-order Element With Element mentioning

confidence: 99%

Section: Stiffness Formulation For Higher-order Element With Element mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Iu¹

2016

Volume 12 Number 4

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Nonlinear fire analysis of steel structure using equivalent thermal load procedure for thermal geometrical change

2016

Fire Safety Journal

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Nonlinear analysis for the pre- and post-yield behaviour of a composite structure with the refined plastic hinge approach

2016

Journal of Constructional Steel Research

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Generalised element load method for first- and second-order element solutions with element load effect

Cited by 4 publications

References 32 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

Nonlinear fire analysis of steel structure using equivalent thermal load procedure for thermal geometrical change

Nonlinear analysis for the pre- and post-yield behaviour of a composite structure with the refined plastic hinge approach

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