Finite-element implementation for nonlinear static and dynamic frame analysis of tapered members

Bai, Rui; Liu, Si Wei; Chan, Siu Lai

doi:10.1016/j.engstruct.2018.05.088

Cited by 19 publications

(4 citation statements)

References 28 publications

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“…In the direct analysis method, advanced computational techniques, which consider the actual stiffness, mass distributions, and load patterns of the structure, are employed [112]. The method considers the second-order effects in the analysis in order to ensure that members can be directly designed according to the section bearing capacity without using effect length factors.…”

Section: Direct Analysis Methodsmentioning

confidence: 99%

Non-Linear Behavior and Design of Steel Structures: Review and Outlook

Zhang,

Chen,

Bai

et al. 2023

Buildings

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The high strength and stiffness-to-weight ratios of structural steel often result in relatively slender members and systems, which are governed to a great extent by stability limit states. However, predicting the stability of slender structures is difficult due to various inherent uncertainties in material and geometry. Generally, structural and member stabilities are nonlinear problems that cannot be directly evaluated based on the section strength using conventional analysis method. Nonlinear behaviors are basically categorized as materially and geometrically nonlinear, which can be observed at the cross-sectional, member, and frame levels. To provide a comprehensive understanding of the current state-of-the-art non-linear behavior and design of steel structures and to identify key areas for future research and development, this paper presents a review on the materially and geometrically nonlinear effects of steel structures. A discussion of the effects of material yielding accentuated by the presence of residual stresses, initial imperfections, and end conditions will be conducted. The stiffness reduction due to second-order effects and material yielding will be illustrated. Moreover, current and emerging design approaches that consider nonlinear responses will also be reviewed and evaluated. Lastly, with the development of modern flexible and complex steel structures, which sometimes violate fundamental assumptions of the current stability design method, the application of advanced analysis and design methods will be explored.

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Section: Direct Analysis Methodsmentioning

confidence: 99%

Non-Linear Behavior and Design of Steel Structures: Review and Outlook

Zhang,

Chen,

Bai

et al. 2023

Buildings

Self Cite

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“…Under this circumstance, the unbalanced forces are used as the applied external loads to act on the structural system until the convergence criterion is satisfied. This Newton‐Raphson incremental‐iterative procedure has been successfully used in various types of nonlinear problems 26–30 . The element formulations and the nonlinear analysis method for pile element have been implemented within CloudSAP 31…”

Section: Numerical Implementation Of Pile Elementsmentioning

confidence: 99%

Numerical formulation and implementation of Euler‐Bernoulli pile elements considering soil‐structure‐interaction responses

Wan

Liu

et al. 2020

Num Anal Meth Geomechanics

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Summary Pile serves as an essential component for transferring loads from superstructures to the soil ground. Proper consideration of soil‐structure interaction (SSI) responses is crucial in evaluating the pile capacity and deflections under external loads. In the current design practices, semi‐empirical or linear‐elastic analyses are utilized, which are often overly conservative and unable to properly consider the nonlinear SSI responses. Thus, this paper presents a new Euler‐Bernoulli pile element for robustly and efficiently simulating the piles considering the SSI responses. The nonlinear springs distributed continuously along with the pile are directly integrated into the element formulations. A quasi‐analytical solution based on the Gauss‐Legendre method is utilized in the summation processes of the total potential energy to significantly simplify the mathematical expressions and ease difficulties in programming. The element tangent stiffness matrix and secant relations are respectively formulated for predicting the displacement and eliminating the accumulative errors in a Newton‐Raphson incremental‐iterative numerical procedure. Because a pile might exhibit large deflections in soft soils, the kinematic motion description using the Updated Lagrangian (UL) approach is developed where the equilibrium conditions are determined by referring to the last configurations. Finally, several examples are provided to validate the accuracy and efficiency of the proposed method.

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“…To manufacture tapered beams, modern technologies such as 3D printing and automated welding can shape beam-like structures of complex geometry. As a result, more cost-efficient structural elements can be produced by optimizing stiffness distributions (Timoshenko and Young 1945;Bai et al 2018;Vo et al 2021) while meeting design criteria. Regarding the manufacture of tapered composite laminates, two methods are employed: ply drop-off and variable prepreg tape spreading.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, more cost-efficient structural elements can be produced by optimizing stiffness distributions (Timoshenko and Young 1945 ; Bai et al. 2018 ; Vo et al. 2021 ) while meeting design criteria.…”

Section: Introductionmentioning

confidence: 99%

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

Vilar

Hadjiloizi

Masjedi

2022

Int J Mech Mater Des

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Emerging manufacturing technologies, including 3D printing and additive layer manufacturing, offer scope for making slender heterogeneous structures with complex geometry. Modern applications include tapered sandwich beams employed in the aeronautical industry, wind turbine blades and concrete beams used in construction. It is noteworthy that state-of-the-art closed form solutions for stresses are often excessively simple to be representative of real laminated tapered beams. For example, centroidal variation with respect to the neutral axis is neglected, and the transverse direct stress component is disregarded. Also, non-classical terms arise due to interactions between stiffness and external load distributions. Another drawback is that the external load is assumed to react uniformly through the cross-section in classical beam formulations, which is an inaccurate assumption for slender structures loaded on only a sub-section of the entire cross-section. To address these limitations, a simple and efficient yet accurate analytical stress recovery method is presented for laminated non-prismatic beams with arbitrary cross-sectional shapes under layerwise body forces and traction loads. Moreover, closed-form solutions are deduced for rectangular cross-sections. The proposed method invokes Cauchy stress equilibrium followed by implementing appropriate interfacial boundary conditions. The main novelties comprise the 2D transverse stress field recovery considering centroidal variation with respect to the neutral axis, application of layerwise external loads, and consideration of effects where stiffness and external load distributions differ. A state of plane stress under small linear-elastic strains is assumed, for cases where beam thickness taper is restricted to $$15^{\circ }$$ 15 ∘ . The model is validated by comparison with finite element analysis and relevant analytical formulations.

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Finite-element implementation for nonlinear static and dynamic frame analysis of tapered members

Cited by 19 publications

References 28 publications

Non-Linear Behavior and Design of Steel Structures: Review and Outlook

Non-Linear Behavior and Design of Steel Structures: Review and Outlook

Numerical formulation and implementation of Euler‐Bernoulli pile elements considering soil‐structure‐interaction responses

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

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