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Here ν is Poisson's ratio, E is Young's modulus, n is a unit vector directed along the direction of extension, m is a unit vector directed perpendicular to the direction of extension. Poisson's ratio has a different number of special directions depending on the type of anisotropy.
k! = k(k–1) ··· (3)(2)(1) is the factorial. The positive real number λ is equal to the expected value of X and also to its variance. [13] = = (). The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. The number of such events that occur during a fixed time interval is ...
2 Poisson's ratio. 3 Bulk modulus. 4 Shear modulus. 5 References. 6 See also. Toggle the table of contents. Elastic properties of the elements (data page) 1 language.
Poisson-type random measures are a family of three random counting measures which are closed under restriction to a subspace, i.e. closed under thinning. They are the only distributions in the canonical non-negative power series family of distributions to possess this property and include the Poisson distribution, negative binomial distribution, and binomial distribution. [1]
where K is the stress intensity factor (with units of stress × length 1/2) and is a dimensionless quantity that varies with the load and geometry. Theoretically, as r goes to 0, the stress σ i j {\displaystyle \sigma _{ij}} goes to ∞ {\displaystyle \infty } resulting in a stress singularity. [ 5 ]
E 1 and E 2 are the Young's moduli in the 1- and 2-direction and G 12 is the in-plane shear modulus. v 12 is the major Poisson's ratio and v 21 is the minor Poisson's ratio. The flexibility matrix [S] is symmetric. The minor Poisson's ratio can hence be found if E 1, E 2 and v 12 are known.
where is the flexural modulus (in Pa), is the second moment of area (in m 4), is the transverse displacement of the beam at x, and () is the bending moment at x. The flexural rigidity (stiffness) of the beam is therefore related to both E {\displaystyle E} , a material property, and I {\displaystyle I} , the physical geometry of the beam.
The finite Poisson's ratio can be found by integrating the infinitesimal Poisson's ratio from zero out to the final . Linear elasticity assumes infinitesimally small strain variations about ε x {\displaystyle \varepsilon _{x}} .