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A living hinge or integral hinge is a thin flexible hinge (flexure bearing).It is made from the same material as the two rigid pieces it connects. It is typically thinned or cut to allow the rigid pieces to bend along the line of the hinge.
The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.
In geotechnical engineering, a discontinuity (often referred to as a joint) is a plane or surface that marks a change in physical or chemical characteristics in a soil or rock mass. A discontinuity can be, for example, a bedding , schistosity , foliation , joint , cleavage , fracture , fissure , crack, or fault plane.
The omission of the expansion joint removes a pathway for the penetration of chloride-bearing road salts to the bridge's sub-structure. In the United Kingdom there is a presumption that most new short to medium length bridges will be of the integral type. [citation needed] An early example of an integral bridge is masonry arch bridge.
Integration by substitution, a method for computing integrals, by using a change of variable; Symbolic integration, the computation, mostly on computers, of antiderivatives and definite integrals in term of formulas; Integration, the computation of a solution of a differential equation or a system of differential equations:
An example of a torsion-free module that is not flat is the ideal (x, y) of the polynomial ring k[x, y] over a field k, interpreted as a module over k[x, y]. Any torsionless module over a domain is a torsion-free module, but the converse is not true, as Q is a torsion-free Z-module that is not torsionless.
Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.
Integration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate this single function into a product of two functions u(x)v(x) such that the residual integral from the integration by parts formula is easier to evaluate than the ...