Mechanics Of Materials Saouma Episode 12 ppt

... quadratic expression of W and obtain for instance T 12 = ∂W ∂E 12 =2c 6 + c 1 112 E 11 + c 2 212 E 22 + c 3 312 E 33 + c 121 2 E 12 + c 122 3 E 23 + c 123 1 E 31 (18.32) if the stress must also be zero ... c 2233 E 22 E 33 +2c 2223 E 22 E 23 +2c 2231 E 22 E 31 +2c 2 212 E 22 E 12 + 1 2 c 3333 E 2 33 +2c 3323 E 33 E 23 +2c 3331 E 33 E 31 +2c 3 312 E 33 E 12 +2c 2323 E 2 23...

Ngày tải lên: 13/08/2014, 17:20

... steel E 2,000 = 30,000 2,000 =15ksi Victor Saouma Mechanics of Materials II Draft 12. 2 Griffith Theory 5 x h Figure 12. 4: Influence of Atomic Misfit on Ideal Shear Strength and from basic elasticity τ = Gγ xy (12. 21) and, Fig. 12. 4 γ xy = ... 13.7: Effect of Geometry and Load on Crack Stability, (Gdoutos 1993) Victor Saouma Mechanics of Materials II Draft 6 THEORETICAL...

Ngày tải lên: 13/08/2014, 17:20

... B 11 C 12 D 12 + B 12 C 11 D 21 + B 12 C 12 D 22 A 12 = B 11 C 11 D 11 + B 11 C 12 D 12 + B 12 C 11 D 21 + B 12 C 12 D 22 A 21 = B 21 C 11 D 11 + B 21 C 12 D 12 + B 22 C 11 D 21 + B 22 C 12 D 22 A 22 = ... Loading 5 Victor Saouma Mechanics of Materials II Draft iv Victor Saouma Mechanics of Materials II Draft Part I CONTINUUM MECHANICS Draft viii...

Ngày tải lên: 13/08/2014, 17:20

... a 3 3 V 3 (1.47) Victor Saouma Mechanics of Materials II Draft 4 KINETICS The vector sum of all external forces acting on the free body is equal to the rate of change of the total momentum 2 . 12 The total ... the projections of v onto the coordinate axes, Fig. 1.1. 12 The unit vector in the direction of v is given by e v = v v =cosαi +cosβj +cosγk (1.15) Victor Saouma...

Ngày tải lên: 13/08/2014, 17:20

... (3.26-b) Victor Saouma Mechanics of Materials II Draft 10 KINETICS Figure 2.5: Differential Shell Element, Stresses Figure 2.6: Differential Shell Element, Forces Victor Saouma Mechanics of Materials ... height of Victor Saouma Mechanics of Materials II Draft 10 MATHEMATICAL PRELIMINARIES; Part II VECTOR DIFFERENTIATION that is [∇v] ij gives the rate of change of t...

Ngày tải lên: 13/08/2014, 17:20

... 4 .12- c. Partial differentiation of Eq. 4 .12- c with respect to X j produces the material displacement gradient ∂u i ∂X j = ∂x i ∂X j − δ ij or J ≡ u∇ X = F −I (4.44) Victor Saouma Mechanics of Materials ... E 22 = ∂u 2 ∂X 2 (4.86) Victor Saouma Mechanics of Materials II Draft 4.2 Strain Tensor 19 Therefore the off diagonal terms of the linear strain tensor represent one h...

Ngày tải lên: 13/08/2014, 17:20

... n (2) ·n (2) =1) n (2) =  001  (4.178) Victor Saouma Mechanics of Materials II Draft 40 KINEMATIC Figure 4 .12: Wheatstone Bridge Configurations Victor Saouma Mechanics of Materials II Draft Chapter 5 MATHEMATICAL PRELIMINARIES; ... obtain  Ω Φ ∂Ψ ∂x dΩ=  Γ ΦΨn x dΓ −  Ω ∂Φ ∂x ΨdΩ (5.11) Victor Saouma Mechanics of Materials II Draft 26 KINEMATIC Example 4 -12: Pola...

Ngày tải lên: 13/08/2014, 17:20

... obtain c ijkm =         c 1111 c 1122 c 1133 c 1 112 00 c 2222 c 2233 c 2 212 00 c 3333 c 3 312 00 c 121 2 00 SYM. c 2323 c 2331 c 3131         (7 .12) we now have 13 nonzero coefficients. Victor Saouma Mechanics of Materials ... =  dq θ  rev (6.44) Victor Saouma Mechanics of Materials II Draft 12 FUNDAMENTAL LAWS of CONTINUUM MECHANICS Victor Sao...

Ngày tải lên: 13/08/2014, 17:20

... the strain componenet of an elementary volume of an unconstrained isotropic body are given by E (Θ) ij = α(Θ − Θ 0 )δ ij (7.57) Victor Saouma Mechanics of Materials II Draft 12 CONSTITUTIVE EQUATIONS; ... = E 3 ,and 1 K = 0 or elastic incompressibility. 39 The elastic properties of selected materials is shown in Table 7.2. Victor Saouma Mechanics of Materials II Draf...

Ngày tải lên: 13/08/2014, 17:20

... the loading that each particle of the elastic sphere will expereince only a radial displacement Victor Saouma Mechanics of Materials II Draft Part III FRACTURE MECHANICS Draft 9.2 Airy Stress ... that in certain literature, (specially the one of Lehigh University), instead of K = f(g)σ √ πa, k = f (g)σ √ a is used. Victor Saouma Mechanics of Materials II Draft Draft 8...

Ngày tải lên: 13/08/2014, 17:20