Sentence examples for middle surface and from inspiring English sources

An uncertainty of some duration arose in the theory from the fact that the final partial differential equation for the transverse displacement is such that it is impossible to prescribe, simultaneously, along an unsupported edge of the plate, both the twisting moment per unit length of middle surface and the transverse shear force per unit length.

Another important feature is that the present technique directly estimates the rotation of the normal of the middle surface, and not the rotation of the middle surface.

An iterative numerical procedure for determining the true middle surface and the corresponding thickness at each cross-section around the circumference is established.

where u0, v0, and w0 are the displacement components of the middle surface, and ϕ x and ϕ θ are changes in the slope of the normal to the middle surface around θ and x axes, respectively.

First, the location of neutral surface is defined with respect to the position of the middle surface and then the governing bending equations are derived using the principle of virtual work.

Since ( varepsilon_{r}^{0},varepsilon_{theta }^{0},gamma_{rtheta }^{0},kappa_{r},, kappa_{theta },, kappa_{rtheta },gamma_{rz}^{0},gamma_{theta z}^{0} ) are middle surface strains and curvatures and not functions of z, they can be taken out of the integration signs.

The middle surface of shells and panels is described by means of the differential geometry tool.

The geometry description of the middle surface of shells and panels is computed by means of differential geometry tools.

The functions θ x, θ y are the rotations of the normals to the middle surface about y and x axes, respectively.

In particular, an exact finite strain analysis is given – in addition to the usual strain tensor associated to the middle surface, the second and third fundamental forms of the middle surface of the deformed thin plate are also maintained in the analysis.

A 2D higher-order shear deformation theory is also proposed and the differential geometry is used to define the arbitrary shape of the middle surface of shells and panels with different curvatures.