Theory of Elasticity |
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Page 61
... bending of a flat plate is a second- order effect in comparison with the bending deflection itself . This is seen , for example , from the fact that the strain tensor ( 14.1 ) , which gives this stretching , is quadratic in . The ...
... bending of a flat plate is a second- order effect in comparison with the bending deflection itself . This is seen , for example , from the fact that the strain tensor ( 14.1 ) , which gives this stretching , is quadratic in . The ...
Page 62
... bending energy is small compared with the stretching energy , it is clear that , if any given shell permits deformation without stretching , then such defor- mations will , in general , actually occur when arbitrary external forces act ...
... bending energy is small compared with the stretching energy , it is clear that , if any given shell permits deformation without stretching , then such defor- mations will , in general , actually occur when arbitrary external forces act ...
Page 72
... bending occur in the zx - plane . † σxx As in the bending of plates and the twisting of rods , the external forces on the sides of a thin bent rod are small compared with the internal stresses , and can be taken as zero in determining ...
... bending occur in the zx - plane . † σxx As in the bending of plates and the twisting of rods , the external forces on the sides of a thin bent rod are small compared with the internal stresses , and can be taken as zero in determining ...
Contents
FUNDAMENTAL EQUATIONS 1 The strain tensor | 1 |
2 The stress tensor | 4 |
3 The thermodynamics of deformation | 8 |
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adiabatic angle axes axis bending biharmonic equation boundary conditions centre clamped coefficient components constant corresponding cross-section crystal crystallite curl curvature deflection derivatives Determine the deformation displacement vector edge elastic wave element equations of equilibrium equations of motion expression external forces fluid force F formula free energy frequency function given gives grad div Hence hydrostatic compression integral internal stresses isotropic isotropic body length Let us consider longitudinal waves medium modulus non-zero perpendicular plane plate PROBLEM quadratic quantities radius region of contact respect result rotation satisfies shear shell small compared SOLUTION strain tensor stress tensor stretching Substituting suffixes symmetry temperature theory of elasticity thermal conduction thin torsion transverse waves undeformed unit volume values velocity of propagation vibrations wave vector x-axis xy-plane Young's modulus z-axis zero диі дхду дхі дхк