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The curve () describes the deflection of the beam in the direction at some position (recall that the beam is modeled as a one-dimensional object). q {\displaystyle q} is a distributed load, in other words a force per unit length (analogous to pressure being a force per area); it may be a function of x {\displaystyle x} , w {\displaystyle w ...
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. [1] [2] A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies' surfaces (known as normal stress) and frictional stresses acting tangentially between the surfaces (shear stress).
The starting point is the relation from Euler-Bernoulli beam theory = Where is the deflection and is the bending moment. This equation [7] is simpler than the fourth-order beam equation and can be integrated twice to find if the value of as a function of is known.
The cantilever method is an approximate method for calculating shear forces and moments developed in beams and columns of a frame or structure due to lateral loads. The applied lateral loads typically include wind loads and earthquake loads, which must be taken into consideration while designing buildings.
The Mooney–Rivlin model is a special case of the generalized Rivlin model (also called polynomial hyperelastic model [6]) which has the form =, = (¯) (¯) + = with = where are material constants related to the distortional response and are material constants related to the volumetric response.
The quantity has units of force per unit length. The quantity M {\displaystyle M} has units of moment per unit length. For isotropic , homogeneous , plates with Young's modulus E {\displaystyle E} and Poisson's ratio ν {\displaystyle \nu } these equations reduce to [ 2 ]
In general, exact solutions for cantilever plates using plate theory are quite involved and few exact solutions can be found in the literature. Reissner and Stein [ 8 ] provide a simplified theory for cantilever plates that is an improvement over older theories such as Saint-Venant plate theory.
A double-end Euler spiral. The curve continues to converge to the points marked, as t tends to positive or negative infinity. An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.