工程中常用的一类厚度远小于平面尺寸的板件。厚度虽小，但横向剪力所引起的变形和弯曲变形属同一量级，在分析静载荷下的应力和变形时，仍须考虑横向剪切效应，垂直于板面方向的正应力则可忽略。

A kind of plate with thickness less than the plane size is commonly used in engineering. The thickness is small, but caused by transverse shear deformation and bending deformation is the same order of magnitude, in the analysis under static load stress and deformation, considered the effect of transverse shear, perpendicular to the direction of the surface normal stress can be ignored.

在分析动载荷下的应力和变形时，除考虑横向剪切效应外，还须考虑微段的惯性力和阻尼力矩。中厚板在机械工业中早已有广泛应用。近年来由于高压、高温和强辐射的环境要求，工程中板的厚度有所增加，很多板件均改用中厚板理论进行分析。

In the analysis of the stress and deformation under dynamic loading, the inertia force and damping moment should be considered in addition to the transverse shear effect. Medium and heavy plate has been widely used in mechanical industry. In recent years, due to the environmental requirements of high pressure, high temperature and strong radiation, the thickness of the plate has been increased.

若中厚板位于xy平面内，在考虑横向剪力影响并忽略垂直于板面方向（z方向）的正应力情况下,中厚板受z方向分布载荷p的作用的弯曲微分方程式为： 式中ω为板的挠度；t为板厚；ν为泊松比；Qx、Qy分别为x、y方向的横向剪力;Δ为拉斯算符(即)；为弯曲刚度，其中E为弹性模量。

If the plate is located in the XY plane, considering the transverse shear effects and ignore the perpendicular to the plate direction (z direction) of the normal stress condition, differential equation of plate bending by Z direction load distribution function of P is: in Omega is the deflection of plate thickness; t; V for Poisson's ratio; the transverse shear force Qx, Qy were x, Y direction; Delta Operator (i.e. for LAS); for the bending stiffness, the elastic modulus is E.

理论上 可从第一个方程求得ω,再由后两个方程求得Qx、Qy，然后进一步求得弯矩、扭矩。但这一偏微分方程不能直接积分，所以通常用纳维法、瑞利－里兹法、有限差分方法等方法求解。近年来，由于有限元法的发展，出现不少计算中厚板的程序，通过它们可以很方便地求得解答。从结果看，在考虑横向剪切效应后，挠度ω有所增大,自振频率和失稳临界载荷有所降低，板件中内力的变化趋于平缓。这些变化的程度都与板的厚跨比的平方成比例。

In theory, it can be obtained from the first equation, and then Qx and Qy are obtained by the latter two equations. But this partial differential equation can not be directly integral, so usually use Navier method, Rayleigh Ritz method and finite difference method and other methods. In recent years, due to the development of the finite element method, many programs have been developed to calculate the plate. The results show that the deflection is increased, the natural frequency and the critical load are decreased, and the change of the internal force of the plate tends to be gentle. These changes are proportional to the square of the thickness to span ratio of the plate.

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