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Rigidity is the property of a structure that it does not bend or flex under an applied force. The opposite of rigidity is flexibility.In structural rigidity theory, structures are formed by collections of objects that are themselves rigid bodies, often assumed to take simple geometric forms such as straight rods (line segments), with pairs of objects connected by flexible hinges.
The simplest bodies or elements of a multibody system were treated by Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention Lagrange’s formalisms based on minimal coordinates and a second formulation that introduces constraints.
Flexural rigidity is defined as the force couple required to bend a fixed non-rigid structure by one unit of curvature, or as the resistance offered by a structure while undergoing bending. Flexural rigidity of a beam
For rigid pavements, design the pavement to reach a standard flexural stress of 2.75 MPa at the bottom of the cement concrete layer according to Westergaard theory; Calculate the single wheel load, inflated at 1.25 MPa, that would require the same pavement – this is the Derived Single Wheel Load (DSWL)
Additionally, special care must be taken to design the flexure to avoid material yielding or fatigue, both of which are potential failure modes in a flexure design. A leaf spring suspension is an example of a flexure design in automotive engineering.
[citation needed] Other optimization techniques focus topology optimization of the flexure joints by taking as input a rigid mechanism and replacing all the rigid joints with optimized flexure joints. [4] To predict the behavior of the structure, finite-element stress analysis is done to find deformation and stresses over the entire structure.
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Also includes an e-book library of classic texts on mechanical design and engineering. Weinstein, Warren D., "Flexure-Pivot Bearings", Machine Design, Part 1, June 10, 1965, Part 2, July 8, 1965 - Spring rates, bearing types, single and multi-strip design, material types, hysteresis and fatigue; Weinstein, Warren D., "Microperformance of Metals".