Scientific and applied communicationNonlinear elastic beam theory with application in contact problems and variational approaches☆
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Parameter identification in contact problems for Gao beam
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2021, Mathematics and Computers in SimulationA Bernstein Broyden–Fletcher–Goldfarb–Shanno collocation method to solve non-linear beam models
2021, International Journal of Non-Linear MechanicsCitation Excerpt :The Analog Equation Method (AEM) of Katsikadelis was applied by Tsiatas [12] (2010) to solve the non-linear problem of non-uniform beams resting on foundation with linear and non-linear Winkler and linear Pasternak parameters. In 2011, Machalová and Netuka [13] developed a specific variational formulation to solve the non-linear beam model by Gao [14], reformulating the problem as an unconstrained minimization assisted by the employment of a Lagrange multiplier. In 2012, Mohammadpour et al. [15] applied the Homotopy Analysis Method (HAM) to obtain an analytical solution to Euler–Bernoulli beams with non-linear Winkler type foundation.
A rod-beam system with dynamic contact and thermal exchange condition
2021, Applied Mathematics and ComputationCitation Excerpt :Recently, Kirchhoff type multidimensional problems have been mathematically examined by many papers (see, e.g., [9–12] and the references therein). Another well-known nonlinear beam model in the static case was initially proposed by Gao [13] in 1996 and was extended into the dynamic case with frictionless contact or a crack [14–16]. Unlike the standard linear beams, the Gao beams can vibrate about a buckling state.
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This work was supported in part by National Science Foundation Grant DMS-9400565