Consistent linearization for path following methods in nonlinear fe analysis

Schweizerhof, Karl; Wriggers, Peter

doi:10.1016/0045-7825(86)90001-0

Cited by 178 publications

(88 citation statements)

References 17 publications

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“…Two special cases are investigated following the methods developed in References [2,[20][21][22][23] in order to distinguish between two major technically important cases, which have some implications on the solution process. In the ÿrst case the focus is on geometrically non-linear structures with closed chambers loaded by an external loading, controlled by arclength procedures.…”

Section: Non-linear Analysis Using Arc-length Proceduresmentioning

confidence: 99%

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Volume‐dependent pressure loading and its influence on the stability of structures

Rumpel

Schweizerhof

2002

Numerical Meth Engineering

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SUMMARYDeformation-dependent pressure loading on solid structures is created by the interaction of gas with the deformable surface of a structure. Such fairly simple load models are valid for static and quasistatic analyses and they are a very e cient tool to represent the in uence of gas on the behaviour of structures. Completing previous studies on the deformation dependence of the loading with the assumption of inÿnite gas volumes, the current contribution is focusing on the in uence of modiÿcations of the size and shape of a ÿnite volume containing the gas in particular on the stability of structures. The linearization of the corresponding virtual work expression necessary for a Newton-type solution leads to additional terms for the volume dependence. Investigating these terms the conservativeness of the problem can be proven by the symmetry of the linearized form. The discretization with ÿnite elements leads to standard sti ness matrix forms plus the so-called load sti ness matrices and a rankone update for each enclosed volume part, if the loaded surface segments are identical with element surfaces. Some numerical examples show ÿrst the e ectiveness of the approach and the necessity to take the corresponding terms in the variational expression and in the following linearization into account, and second the particular in uence of this term on the stability of structures is shown with some speciÿc examples.

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Section: Non-linear Analysis Using Arc-length Proceduresmentioning

confidence: 99%

“…As control law an iteration on normal surfaces [23] with t as tangent vector on the load de ection curve is chosen…”

Section: Arc-length Controlled Loading On Pressurized Closed Structuresmentioning

confidence: 99%

Volume‐dependent pressure loading and its influence on the stability of structures

Rumpel

Schweizerhof

2002

Numerical Meth Engineering

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“…In order to obtain the whole equilibrium path, including the unstable configurations, an arclength algorithm based on Schweizerhof and Wriggers [19] is used. The method controls neither the load nor the displacement but traces the equilibrium configurations, both stable and unstable ( Figure 7), with increments in the length of an arc on this curve.…”

Section: Path Following Analysis Using An Arclength Methodsmentioning

confidence: 99%

Numerical pathologies in snap-through simulations

Chandra

Stanciulescu

Eason

et al. 2012

Engineering Structures

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Aircraft structures operating in severe environments may experience snap-through, causing the curvature on part or all of the structure to invert inducing fatigue damage. This paper examines the performance of beam and continuum nonlinear finite element formulations in conjunction with several popular implicit time stepping algorithms to assess the accuracy and stability of numerical simulations of snap-through events. Limitations for the structural elements are identified and we provide examples of interaction between spatial and temporal discretizations that affect the robustness of the overall scheme and impose strict limits on the size of the time step. These limitations need to be addressed in future works in order to develop accurate, robust and efficient simulation methods for response prediction of structures encountering extreme environments.

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“…Initially, Figure 4A illustrates the static analysis carried out with a classic structural system known as Lee Frame (Schweizerhof and Wriggers, 1986). By its sensitivity to second-order effects, this slender frame is commonly used to validate the nonlinear solution strategies and the geometric nonlinear finite element formulations.…”

Section: Some Modeling Using the Cs-asamentioning

confidence: 99%

CS-ASA: a new computational tool for advanced analysis of steel frames

Silva

Prado²,

Silveira

2013

Rem: Rev. Esc. Minas

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Esse trabalho apresenta uma nova ferramenta computacional, para análise avançada estática e dinâmica de estruturas de aço reticuladas planas, desenvolvida com base no Método dos Elementos Finitos. Duas fontes de não linearidades são consideradas nas análises: a geométrica, que considera os efeitos da deslocabilidade da estrutura; e a física, causada, principalmente, pelas características mecânicas dos materiais utilizados na construção civil. Imperfeições relacionadas com o carregamento, geometria do sistema e tensões residuais podem, também, serem consideradas. Para se ilustrarem alguns dos recursos e análises que diferenciam essa ferramenta dos programas comerciais existentes, a estabilidade estática e dinâmica de alguns sistemas estruturais, com ligações rígidas e semirrígidas, é avaliada. As respostas obtidas por outros pesquisadores são usadas, para validar as formulações e as metodologias de solução não linear, implementadas nessa ferramenta, e para atestar a eficiência desse programa caseiro de análise estrutural. Palavras-chave:

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Consistent linearization for path following methods in nonlinear fe analysis

Cited by 178 publications

References 17 publications

Volume‐dependent pressure loading and its influence on the stability of structures

Volume‐dependent pressure loading and its influence on the stability of structures

Numerical pathologies in snap-through simulations

CS-ASA: a new computational tool for advanced analysis of steel frames

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