A total Lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements. Part II: Arches, frames and axisymmetric shells

Oliver, J.; Oñate, Eugenio

doi:10.1002/nme.1620230209

Cited by 20 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The modulus of elasticity and Poisson's ratio of the purely elastic material are Downloaded by [Ferdowsi University] at 23:06 11 February 2012 206 8324 × 10 6 N/m 2 and 0.3, respectively. The finite element analysis of this thinwalled structure is based on total Lagrangian formulation of axisymmetric shells (Oliver and Onate, 1986). This formulation allows for large displacements and large rotations of the structures.…”

Section: Building Framementioning

confidence: 99%

Timestep Selection for Dynamic Relaxation Method

Rezaiee‐Pajand

Kadkhodayan

Alamatian

2012

Mechanics Based Design of Structures and Machines

View full text Add to dashboard Cite

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

show abstract

Section: Building Framementioning

confidence: 99%

Timestep Selection for Dynamic Relaxation Method

Rezaiee‐Pajand

Kadkhodayan

Alamatian

2012

Mechanics Based Design of Structures and Machines

View full text Add to dashboard Cite

show abstract

“…The header line defines certain intervals i a :i b . Each interval represents a group of pseudotime steps ∆t i which show [16] a comparable convergence behavior. Limit i a is the smallest while i b is the largest number of equilibrium iterations i required by this group of incremental steps.…”

Section: Examplesmentioning

confidence: 99%

“…Numerical stability is an advantage of the method proposed here. 9.4 Shallow arch from Oliver and Onate [16] Figure 16 shows the geometry of the shallow arch examined by Oliver and Onate [15,16]. The arch is discretized using 16 solid elements.…”

Section: Deviations Of the Solution Path Obtained By The Arc-length Amentioning

confidence: 99%

Postbuckling analysis stabilized by penalty springs and intermediate corrections

Müller¹

2008

Comput Mech

View full text Add to dashboard Cite

Whenever a critical point in a non-linear finite element analysis is reached, an implicit Newton procedure is prevented from proceeding until the stiffness matrix is stabilized. Most stabilization procedures result in a damped Newton scheme. This can cause a reduced convergence rate. Based on documented stabilization strategies, an iterative procedure to reduce negative impact on the convergence rate resulting from the damping is to be proposed here. This will be done by a corrector iteration carried out between two successive equilibrium iterative steps. The equilibrium iteration is a Newton-Raphson scheme. Since the stiffness matrix has already been factorized within the preceding standard equilibrium iterative step, the stiffness matrix will be held constant during the corrector iteration, which in turn allows for a computational efficient treatment of the additional iterations. The proposed procedure has been strongly driven by Wright and Gaylord's (ASCE J. Struct. Div., 94, 1143-1163 investigation.

show abstract

Post-Buckling Analysis With Frictional Contacts Combining Complementarity Relations and an Arc-Length Method

Koo

Kwak

1996

Int. J. Numer. Meth. Engng.

View full text Add to dashboard Cite

A linear complementarity problem formulation combined with an arc-length method is presented for post-buckling analysis of geometrically non-linear structures with frictional contact constraints. The arc-length method with updated normal plane constraint is used to trace the equilibrium paths of the structures after limit points. Under the proportional loading assumption, the unknown load scale parameter used in the arc-length method is expressed in terms of contact forces, and eliminated to formulate as a linear complementarity problem. The unknown contact variables such as contact status and contact forces can be directly solved in this formulation without any ad hoc technique. Complicated non-linear buckling behaviours, such as snap-buckling, can be efficiently solved by the developed method, as shown by several buckling and post-buckling problems with frictional contact constraints. KEY WORDS post-buckling frictional contact; complementarity; arc-length methodRecently, Kwak et al." -I 3 have derived a linear complementarity problem which is mathematically complete and needs no contact iteration even with friction. This is in contrast with other approaches in the literature such as Kikuchi and Oden,14 well studied in the frame of a variational formulation for friction problems.

show abstract

A total Lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements. Part II: Arches, frames and axisymmetric shells

Cited by 20 publications

References 11 publications

Timestep Selection for Dynamic Relaxation Method

Timestep Selection for Dynamic Relaxation Method

Postbuckling analysis stabilized by penalty springs and intermediate corrections

Post-Buckling Analysis With Frictional Contacts Combining Complementarity Relations and an Arc-Length Method

Contact Info

Product

Resources

About