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  • Hilbert boundary value problem in the theory of plates
    Brešar, France ; Kutnjak, Milan
    The bending of an elastic, homogeneous, isotropic plate of constant thickness 2h is treated. The plane xy of the cartesian coordinate system xyZ lies in the middle plane of the plate. The upper plane ... of the plate (Z=h) is loaded by transverse loading q(x,y). The stress tensor components satisfy the equilibrium equations and Beltrami-Michell compatibility conditions, while the linear Hook's law is valid for the displacements. The general solution is expressed with 5 analytical functions of variable z, the so-called stress functions. We shall denote them by P, ▫$\Omega$▫, ▫$\omega$▫, ▫$varphi$▫, ▫$psi$▫. Function P is defined with transverse loading q(x,y)=1/2Re[P''(z)]. At supposition ▫$\sigma_z={q(x,y)\over{4h^3} Z^3-3h^2Z-2h^3)}$▫, ▫$\sigma_z$▫(Z=h)=-q(x,y), ▫$\sigma_z$▫(Z=-h)=0, ▫$\tau_{xz}$▫(Z=▫$\pm$▫h)=0, ▫$\tau_{yz}$▫(Z=▫$\pm$▫h)=0, the displacementsa are D=u+iv=D▫$_0$▫+D▫$_1$▫Z+D▫$_2$▫Z▫$^2$▫+D▫$_3$▫Z▫$^3$▫+D▫$_5$▫Z▫$^5$▫, w=w▫$_0$▫+w▫$_1$▫Z+w▫$_2$▫Z▫$^2$▫+w▫$_4$▫Z▫$^4$▫. Similar expresions are valid for ▫$\sigma_x$▫, ▫$\sigma_y$▫, ▫$\sigma_z$▫, ▫$\tau_{xy}$▫, ▫$\tau_{xx}$▫, ▫$\tau_{yz}$▫.
    Source: Short communications in mathematics and mechanics, section 1-7, GAMM 99, Annual Meeting, University of Metz, France, April 12-16, 1999 (80, suppl. 2, 2000, S377-S378)
    Type of material - conference contribution
    Publish date - 2000
    Language - english
    COBISS.SI-ID - 5296406

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