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Figure 7.1 Plane stress state in a continuum. In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 ...
The chief advantage of critical plane analysis over earlier approaches like Sines rule, or like correlation against maximum principal stress or strain energy density, is the ability to account for damage on specific material planes. This means that cases involving multiple out-of-phase load inputs, or crack closure can be treated with high ...
The advantages of the Watts-Ford test are that it is convenient for testing thin sheets or strips, it is similar to a rolling process (in manufacturing analyses), frictional effects may be minimized, there is no 'barrelling' as would occur in a cylindrical compression test, and the plane strain deformation eases the analysis. Stress-strain curve
For two-dimensional, plane strain problems the strain-displacement relations are = ; = [+] ; = Repeated differentiation of these relations, in order to remove the displacements and , gives us the two-dimensional compatibility condition for strains
A starting point for solving contact problems is to understand the effect of a "point-load" applied to an isotropic, homogeneous, and linear elastic half-plane, shown in the figure to the right. The problem may be either plane stress or plane strain. This is a boundary value problem of linear elasticity subject to the traction boundary conditions:
This way, the shear stress acting on plane B is negative and the shear stress acting on plane A is positive. The diameter of the circle is the line joining point A and B. The centre of the circle is the intersection of this line with the -axis. Knowing both the location of the centre and length of the diameter, we are able to plot the Mohr ...
In continuum mechanics, the Michell solution is a general solution to the elasticity equations in polar coordinates (,) developed by John Henry Michell in 1899. [1] The solution is such that the stress components are in the form of a Fourier series in θ {\displaystyle \theta } .
Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics , stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other ...