By Erich Cavazos; Robert Khan
This can be an built-in publication of Fracture and Bending Mechanics.
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Additional info for Fracture and bending mechanics
Chapter 8 Peridynamics A ductile fracture of an Al-Mg-Si alloy. A fracture is a mathematical singularity to which the classical equations of continuum mechanics cannot be applied directly Peridynamics offers a numerical method. Peridynamics is a formulation of continuum mechanics that is oriented toward deformations with discontinuities, especially fractures. Purpose of peridynamics The peridynamic theory is based on integral equations, in contrast with the classical theory of continuum mechanics, which is based on partial differential equations.
The beam has an axis of symmetry in the plane of bending. 6. The proportions of the beam are such that it would fail by bending rather than by crushing, wrinkling or sideways buckling. 7. Cross-sections of the beam remain plane during bending. Deflection of a beam deflected symmetrically and principle of superposition Compressive and tensile forces develop in the direction of the beam axis under bending loads. These forces induce stresses on the beam. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam.
For stresses that exceed yield, refer to article plastic bending. At yield, the maximum stress experienced in the section (at the furthest points from the neutral axis of the beam) is defined as the flexural strength. The Euler-Bernoulli equation for the quasistatic bending of slender, isotropic, homogeneous beams of constant cross-section under an applied transverse load q(x) is where E is the Young's modulus, I is the area moment of inertia of the cross-section, and w(x) is the deflection of the neutral axis of the beam.