The conditions for one model are derived for an elastic clamped support of plate-strip. Using the Fuss-Winkler hypothesis the parameters of this support and the relationship between them are defined. Based on the refined theory [1] the governing differential equations are presented for the problem of transversal bending of orthotropic plate of variable thickness, when the effect of transverse shear deformation is taken into account. The specific example of elastically clamped support is considered and qualitative conclusions are given.
On the basis of the refined theory of orthotropic plates of variable thickness, the equations of the beam bending problem are obtained with the simultaneous action of compressive forces and transverse load. It is accepted that the edges of the beam have an elastically clamped support and the reduction of the compressive force by the support due to friction is taking into account. Passing to dimensionless quantities, a certain problem is solved. The stability of a beam is discussed. Based on the results obtained, conclusions are drawn.
The mathematical model of the problem of bending of an elastically clamped beam is constructed on the basis of the refined theory of orthotropic plates of variable thickness. To solve the problem in the case of simultaneous action of its own weight and compressive axial forces, a system of differential equations with variable coefficients is obtained. The effects of transverse shear and the effect of reducing compressive force of the support are also taken into account. Passing on to dimensionless quantities, the specific problem for a beam of linearly varying thickness is solved by the collocation method. The stability of the beam is discussed. The critical values of forces are obtained by varying the axial compressive force. Results are presented in both tabular and graphical styles. Based on the results obtained, appropriate conclusions are drawn.
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