Rigid body concept for geometric nonlinear analysis of 3D frames, plates and shells based on the updated Lagrangian formulation

Yang, Y.B.; Lin, Shu-Ping; Chen, C.S.

doi:10.1016/j.cma.2006.07.013

Cited by 43 publications

(23 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…12, where a good agreement is observed in respect to the predictions of Izzuddin [19] ð&Þ and Yang et al [20] ðJÞ. Fig.…”

Section: Statical Analysissupporting

confidence: 54%

“…We focus, now, on the description of the strain tensor in (20). We refer to the linear approximation of the tensor components, being, as above-mentioned, the geometrical nonlinearity taken into account by the definition of the deformative invariants.…”

Section: Energetic Quantities Definitionmentioning

confidence: 99%

“…In the dynamical case we refer to (20) expressions with temporal dependence on the displacement vector u and to the Tð _ uÞ kinetic energy:…”

Section: Energetic Quantities Definitionmentioning

confidence: 99%

See 2 more Smart Citations

A finite element approach to statical and dynamical analysis of geometrically nonlinear structures

Lopez

Sala

2010

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

“…12, where a good agreement is observed in respect to the predictions of Izzuddin [19] ð&Þ and Yang et al [20] ðJÞ. Fig.…”

Section: Statical Analysissupporting

confidence: 54%

Section: Energetic Quantities Definitionmentioning

confidence: 99%

See 1 more Smart Citation

A finite element approach to statical and dynamical analysis of geometrically nonlinear structures

Lopez

Sala

2010

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

“…Basically the same ideas have been demonstrated to be capable of solving the nonlinear and postbuckling responses of structures as complicated as the three-dimensional frames, plates and shells in Ref. [5].…”

Section: Introductionmentioning

confidence: 88%

“…Such a strategy allows us to circumvent the complicated procedure of formulation for nonlinear elements. The advantage will become more obvious when dealing with the complicated problems of three-dimensional beams, plates, and shells [5], for which the geometric stiffness matrix cannot be derived in a straightforward manner.…”

Section: Predictor and Corrector For Incremental-iterative Analysismentioning

confidence: 99%

Solution strategy and rigid element for nonlinear analysis of elastically structures based on updated Lagrangian formulation

Yang

Lin

Leu

2007

Engineering Structures

Self Cite

View full text Add to dashboard Cite

A Woodbury solution method for efficient seismic collapse analysis of space truss structures based on hybrid nonlinearity separation

2021

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

This study presents a fast algorithm for collapse behavior simulation of space truss structures under extreme earthquake excitation by introducing the Woodbury formula to efficiently solve the structural response caused by material and geometric nonlinearity (hybrid nonlinearity). The Woodbury formula, which is an efficient tool in mathematics for solving low-rank perturbation problems, has successfully been used to improve the efficiency of local material nonlinear analysis but still has difficulties with seismic collapse analysis in which geometric nonlinearity should be considered. In this study, by implementing stiffness matrix decomposition according to the unchanged reference configuration, the effects of hybrid nonlinearity on the change in tangent stiffness of truss structures are uniformly formulated in the form of hybrid nonlinear perturbation to the reference elastic stiffness. Thus, a hybrid nonlinearity separated governing equation can be established, in which the hybrid nonlinear behaviors are depicted by the additional nonlinear degrees of freedom (NLDOFs) separated from the reference system. This allows for employing the Woodbury formula to perform seismic collapse analysis of space truss structures for avoiding the repeated updating of the global stiffness. To overcome the adverse effect of the large NLDOF number caused by the global characteristics of geometric nonlinearity on the efficiency advantages of the Woodbury formula during seismic collapse analysis, an element state judgment strategy and an adaptive restart mechanism are presented to activate only a small number of NLDOFs within critical local regions. The accuracy and efficiency of the proposed method are verified by two numerical examples.

show abstract

Rigid body concept for geometric nonlinear analysis of 3D frames, plates and shells based on the updated Lagrangian formulation

Cited by 43 publications

References 15 publications

A finite element approach to statical and dynamical analysis of geometrically nonlinear structures

A finite element approach to statical and dynamical analysis of geometrically nonlinear structures

Solution strategy and rigid element for nonlinear analysis of elastically structures based on updated Lagrangian formulation

A Woodbury solution method for efficient seismic collapse analysis of space truss structures based on hybrid nonlinearity separation

Contact Info

Product

Resources

About