弹性力学-E-01-课件.ppt

The tension test is the standard test for determine E, the elastic or Young’s modulus. Test that load a cylindrical specimen in torsion are used to measure the shear modulus G. Knowing E and G, Poisson’s ratio may be obtained from the relationship we derived in the previous section. Mechanics: branch of physics concerned with motion and body deformation created by mechanical disturbance or forces. Applied Mechanics: science of applying the principles of mechanics to design and analysis of mechanical system. Applied Mechanics – Rigid Body Mechanics Statics Dynamics – Kinematics, – Kinetics – Deformable Body Mechanics Elasticity Plasticity Viscoelasticity – Fluid Mechanics Liquids Gases Since forces and moments are vectors, with inherent directionality, it is frequently useful for decompose into individual components: 应力点的概念: 不同点处应力不同。 应力面的概念：同一点处不同截面上的应力不同。 应力必须指明是哪点、哪个截面上的应力。 Complementary Shear Stress（剪应力互等）Consider a rectangular block of unit thickness and suppose shear stresses τ1, act on BC and AD. The forcesτ1 *AD andτ1 * BC form a couple of magnitudeτ1 * AD * AB and the block is not in equilibrium. There must bean equal and opposite couple formed by shear stresses on AB and CD. Stresses on oblique planes:（斜面上的应力） Consider rotating the element ABCD by an angle θ to the x-axis so that it now has axes of x’ and y’ orientated at angleθto the x and y axes. To determine the new stressesσx’,σy’ andτx’y’ on the element in terms of the original stresses consider the free body diagram of a prismatic element ADE and the stresses acting on it are as shown in the Figure. The normal stress σx’ and shear stress τx’y’ act on the plane AE and maintain the equilibrium of the prismatic element. Transformation of Stresses（应力变换） The actual values of the 6 stress components in the stress matrix