Mixed finite element solutions to contact problems of nonlinear Gao beam on elastic foundation

Gao, David Yang; Machalová, Jitka; Netuka, Horymír

doi:10.1016/j.nonrwa.2014.09.012

Cited by 19 publications

(10 citation statements)

References 16 publications

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“…The Euler-Bernoulli beam model enriched with this nonlinear term was studied in [15], [17], [26], [27], [23]. The Gao beam model with the normal compliance contact condition was introduced in a recent paper [11].…”

Section: Introductionmentioning

confidence: 99%

Control variational method approach to bending and contact problems for Gao beam

Machalová¹,

Netuka²

2017

Appl.Math.

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Section: Introductionmentioning

confidence: 99%

Control variational method approach to bending and contact problems for Gao beam

Machalová¹,

Netuka²

2017

Appl.Math.

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“…If the contact is modeled with a normal compliance condition , we can obtain the mathematical description for problems with deformable obstacle, and this description has a form of nonlinear equation . In Gao et al [2] the Gao beam resting on a deformable foundation was studied. More about normal compliance conditions can be found for instance in Shillor et al [3] or Sofonea and Matei [1].…”

Section: Introductionmentioning

confidence: 99%

Solution of contact problems for Gao beam and elastic foundation

Machalová

Netuka

2017

Mathematics and Mechanics of Solids

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This paper presents mathematical formulations and a solution for contact problems that concern the nonlinear beam published by Gao (Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech Res Commun 1996; 23: 11–17) and an elastic foundation. The beam is subjected to a vertical and also axial loading. The elastic deformable foundation is considered at a distance under the beam. The contact is modeled as static, frictionless and using the normal compliance contact condition. In comparison with the usual contact problem formulations, which are based on variational inequalities, we are able to derive for our problem a nonlinear variational equation. Solution of this problem is realized by means of the so-called control variational method. The main idea of this method is to transform the given contact problem to an optimal control problem, which can provide the requested solution. Finally, some results including numerical examples are offered to illustrate the usefulness of the presented solution method.

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“…we obtain the problem which was studied in [14] and the analogous one in the papers [15,16] for a nonlinear beam. Another situation occurs when the beam is resting on a rigid foundation.…”

Section: Contact Problems For Classical Beammentioning

confidence: 99%

Solution of Contact Problems for Nonlinear Gao Beam and Obstacle

Machalová

Netuka²

2015

Journal of Applied Mathematics

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Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.

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Mixed finite element solutions to contact problems of nonlinear Gao beam on elastic foundation

Cited by 19 publications

References 16 publications

Control variational method approach to bending and contact problems for Gao beam

Control variational method approach to bending and contact problems for Gao beam

Solution of contact problems for Gao beam and elastic foundation

Solution of Contact Problems for Nonlinear Gao Beam and Obstacle

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