Analysis of certain unilateral problems in von karman plate theory by a penalty method-part 1. A variational principle with penalty

Ohtake, Kunihiko; Oden, J. Tinsley; Kikuchi, Noboru

doi:10.1016/0045-7825(80)90045-6

Cited by 36 publications

(6 citation statements)

References 12 publications

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“…Another well-known approach for constructing contact models is a penalty method. The variational principle with penalty is used for development of variational unilateral contact problem in the works of Ohtake et al [32,33]. The variational model with penalty for buckling was also considered by Muradova and Stavroulakis [36].…”

Section: Contact Models With Elastic Foundationsmentioning

confidence: 99%

“…The classical linear and nonlinear plate equations are the main keys for creating various plate models, including delamination of composite plates (Vasiliev and Morozov [27], Stavroulakis and Panagiotopoulos [28], Storakers and Andersson [29], Xue et al [30], and Haghani et al [31]), contact problems (Ohtake et al [32,33], Borisovich et al [34], and Malekzadeh and Setoodeh [35], Muradova and Stavroulakis [36][37][38][39], Muradova et al [40], Fichera [41]), analysis of buckled plates (Ciarlet and Rabier [3], Caloz and Rappaz [42], Matkowsky; Putnick [43], Chien et al [44], Chien et al [45], Muradova [46][47][48], Dossou and Pierre [49]), etc.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

Muradova

Stavroulakis

2020

Mathematics

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A review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unilateral contact problems with buckling, including models for plates, resting on elastic foundations, and contact models for delaminated composite plates, are formulated. Dynamic nonlinear equations for elastic plates, which possess buckling and contact effects are also presented. Most commonly used boundary and initial conditions are set up. The advantages and disadvantages of analytical, semi-analytical, and numerical techniques for the buckling and contact problems are discussed. The corresponding references are given.

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Section: Contact Models With Elastic Foundationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

Muradova

Stavroulakis

2020

Mathematics

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“…Composite wall panel cross section [11,12] [ 13,14] Fig . Unilateral contact buckling [14] Seide Co [15,16] P. Villaggio [17] K. Ohtake [18,19] A. B. Uy M.A.…”

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confidence: 99%

Progress of unilateral contact buckling of steel skin sheet in composite wall

Liu

Dong

Liu³

2011

2011 Second International Conference on Mechanic Automation and Control Engineering

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Steel-concrete composite wall is a novel composite structure composed of thin sheet steel outer skin filled with light weight concrete. The composite wall panel can be used as bearing member and also as maintenance structural plate, which can satisfy functional requirement of building including bearing capacity, heat insulation and preservation. As a concerned matter in engineering field, investigation progress of unilateral contact buckling of steel skin sheet is presented by summary, analysis and contrast of relevant results.

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“…Only a limited number of attempts have been made. These include the work of Ohtake et al [10] which is based upon von Karman plate theory; and was concerned with the development of variational inequalities to treat contact in plate elements. In the current work, we extend the frictionless contact formulation for shells developed earlier by El-Abbasi and Meguid, [11] to account for frictional contact.…”

mentioning

confidence: 99%

On the treatment of frictional contact in shell structures using variational inequalities

El-Abbasi

Meguid

1999

Int. J. Numer. Meth. Engng.

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SUMMARYA new variational inequality-based formulation is presented for the large deformation analysis of frictional contact in elastic shell structures. The formulations are based on a seven-parameter continuum shell model, which account for the normal stress and strain through the shell thickness and accommodate double-sided shell contact. The kinematic contact conditions are enforced accurately in terms of the physical contacting surfaces of the shell. Large deformations and rotations are accounted for by invoking the appropriate stress and strain measures. Lagrange multipliers are used to ensure that the kinematic contact constraints are accurately satis"ed and that the solution is free from user-de"ned parameters. Three numerical examples are used to verify the developed formulations and algorithms, and test the various aspects of the solution technique.

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Analysis of certain unilateral problems in von karman plate theory by a penalty method-part 1. A variational principle with penalty

Cited by 36 publications

References 12 publications

Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

Progress of unilateral contact buckling of steel skin sheet in composite wall

On the treatment of frictional contact in shell structures using variational inequalities

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