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

Abstract

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.