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The stiffness, , of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as k = F δ {\displaystyle k={\frac {F}{\delta }}} where,
The plate elastic thickness (usually referred to as effective elastic thickness of the lithosphere). The elastic properties of the plate; The applied load or force; As flexural rigidity of the plate is determined by the Young's modulus, Poisson's ratio and cube of the plate's elastic thickness, it is a governing factor in both (1) and (2).
The bending stiffness is the resistance of a member against bending deflection/deformation. It is a function of the Young's modulus E {\displaystyle E} , the second moment of area I {\displaystyle I} of the beam cross-section about the axis of interest, length of the beam and beam boundary condition.
It is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous linear elastic bar. The torsion constant, together with material properties and length, describes a bar's torsional stiffness. The SI unit for torsion constant is m 4.
Stiffness depends upon material properties and geometry. The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law.
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
Approximate specific stiffness for various materials. No attempt is made to correct for materials whose stiffness varies with their density. Material Young's modulus Density (g/cm 3) Young's modulus per density; specific stiffness (10 6 m 2 s −2) Young's modulus per density squared (10 3 m 5 kg −1 s −2) Young's modulus per density cubed ...
For thick plates, we have to consider the effect of through-the-thickness shears on the orientation of the normal to the mid-surface after deformation. Raymond D. Mindlin's theory provides one approach for find the deformation and stresses in such plates. Solutions to Mindlin's theory can be derived from the equivalent Kirchhoff-Love solutions ...