Theory of Elasticity |
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Page 5
... integral over the surface . As we know from vector analysis , the integral of a scalar over an arbitrary volume can be transformed into an integral over the surface if the scalar is the divergence of a vector . In the present case we ...
... integral over the surface . As we know from vector analysis , the integral of a scalar over an arbitrary volume can be transformed into an integral over the surface if the scalar is the divergence of a vector . In the present case we ...
Page 45
... integral in ( 11.6 ) into two , and vary the two parts separately . The first integral can be written in the form S ( ^ △ 5 ) 2 dƒ , where df dx dy is a surface element and △ = d2 / dx2 + d2 / ǝy2 is here ( and in §§13 , 14 ) the two ...
... integral in ( 11.6 ) into two , and vary the two parts separately . The first integral can be written in the form S ( ^ △ 5 ) 2 dƒ , where df dx dy is a surface element and △ = d2 / dx2 + d2 / ǝy2 is here ( and in §§13 , 14 ) the two ...
Page 48
... integrals . The surface integral is The variation Eh3 Δ A2 - P √ ( 12 ( 1 - 0 ) 25 - P / 85 dƒ . — in this integral is arbitrary . The integral can therefore vanish only if the coefficient of 8 is zero , i.e. Eh3 12 ( 1–62 ) -A2 - P ...
... integrals . The surface integral is The variation Eh3 Δ A2 - P √ ( 12 ( 1 - 0 ) 25 - P / 85 dƒ . — in this integral is arbitrary . The integral can therefore vanish only if the coefficient of 8 is zero , i.e. Eh3 12 ( 1–62 ) -A2 - P ...
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