Geodesic
Control variational method approach to bending and contact problems for Gao beam
Applications of Mathematics, Tome 62 (2017) no. 6, pp. 661-677 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper deals with a nonlinear beam model which was published by D. Y. Gao in 1996. It is considered either pure bending or a unilateral contact with elastic foundation, where the normal compliance condition is employed. Under additional assumptions on data, higher regularity of solution is proved. It enables us to transform the problem into a control variational problem. For basic types of boundary conditions, suitable transformations of the problem are derived. The control variational problem contains a simple linear state problem and it is solved by the conditioned gradient method. Illustrative numerical examples are introduced in order to compare the Gao beam with the classical Euler-Bernoulli beam.
This paper deals with a nonlinear beam model which was published by D. Y. Gao in 1996. It is considered either pure bending or a unilateral contact with elastic foundation, where the normal compliance condition is employed. Under additional assumptions on data, higher regularity of solution is proved. It enables us to transform the problem into a control variational problem. For basic types of boundary conditions, suitable transformations of the problem are derived. The control variational problem contains a simple linear state problem and it is solved by the conditioned gradient method. Illustrative numerical examples are introduced in order to compare the Gao beam with the classical Euler-Bernoulli beam.
DOI : 10.21136/AM.2017.0168-17
Classification : 49J15, 49S05, 65K10, 74K10, 74M15
Keywords: nonlinear beam; elastic foundation; contact problem; normal compliance condition; control variational method; finite element method 
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     title = {Control variational method approach to bending and contact problems for {Gao} beam},
     journal = {Applications of Mathematics},
     pages = {661--677},
     year = {2017},
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Machalová, Jitka; Netuka, Horymír. Control variational method approach to bending and contact problems for Gao beam. Applications of Mathematics, Tome 62 (2017) no. 6, pp. 661-677. doi: 10.21136/AM.2017.0168-17

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