Mechanics Of Materials Saouma Episode 7 docx

... elastic incompressibility. 39 The elastic properties of selected materials is shown in Table 7. 2. Victor Saouma Mechanics of Materials II Draft 7. 2 Stress-Strain Relations in Generalized Elasticity ... obtain Victor Saouma Mechanics of Materials II Draft 7. 4 Fourrier Law 11 where α is the linear coefficient of thermal expansion. 48 Inserting the preceding two equatio...

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 ... v(x)= ∂v(x) ∂x i ·e i (3.13) Victor Saouma Mechanics of Materials II Draft 12 MATHEMATICAL PRELIMINARIES; Part II VECTOR DIFFERENTIATION Victor Saouma Mechanics of...

Ngày tải lên: 13/08/2014, 17:20

... Loading 5 Victor Saouma Mechanics of Materials II Draft iv Victor Saouma Mechanics of Materials II Draft Part I CONTINUUM MECHANICS Draft viii CONTENTS Victor Saouma Mechanics of Materials II Draft iii PREFACE One ... 15 19 .7 Post-Yielding 16 19 .7. 1 Kuhn-Tucker Conditions 16 19 .7. 2 Hardening Rules 17 19 .7. 2.1 Isotropic Hardening . . . 17 19 .7. 2.2 Kinemati...

Ngày tải lên: 13/08/2014, 17:20

... (traction) will be  3 7 6 7 2 7    7 −50 −531 012   =  − 9 7 5 7 10 7  (2.14) and thus t = − 9 7 e 1 + 5 7 e 2 + 10 7 e 3 2.3 Principal Stresses 19 Regardless of the state of stress (as long ... a 2 1 V 2 + 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...

Ngày tải lên: 13/08/2014, 17:20

... ∇ X u    J+J c ) (4 .73 ) or: E 11 = ∂u 1 ∂X 1 (4 .74 -a) E 12 = 1 2  ∂u 1 ∂X 2 + ∂u 2 ∂X 1  (4 .74 -b) ··· = ··· (4 .74 -c) Note the similarity with Eq. 4 .7. Victor Saouma Mechanics of Materials II Draft 10 ... (dX) 2 2dx i dx j (4 .70 ) Victor Saouma Mechanics of Materials II Draft 4.3 Strain Decomposition 21 0 Q Q 0 0 p Q d X d u d x u u P 0 P Figure 4 .7: Relative...

Ngày tải lên: 13/08/2014, 17:20

... 3D Out[12]= i k j j j j j j j 0 .70 7 0 .70 7 0. -0 .70 7 0 .70 7 0. 0. 0. 1. y { z z z z z z z m−polar.nb Victor Saouma Mechanics of Materials II Draft 4 .7 Hydrostatic and Deviatoric Strain 33 Piola−Kirchoff Stress Tensors The ... 3D Out[10]= i k j j j j j j j 0 .70 7 0 .70 7 0. 0 .70 7 2.12 0. 0. 0. 1. y { z z z z z z z In[11]:= U_einverse = N@Inverse@%D,3D Out[11]= i k j j j j j...

Ngày tải lên: 13/08/2014, 17:20

... c 2222 (7. 17- a) c 1133 = c 2233 (7. 17- b) c 2323 = c 3131 (7. 17- c) c 1212 = 1 2 (c 1111 − c 1122 ) (7. 17- d) Victor Saouma Mechanics of Materials II Draft Chapter 6 FUNDAMENTAL LAWS of CONTINUUM MECHANICS 6.1 Introduction 1 ... Mechanics of Materials II Draft 12 FUNDAMENTAL LAWS of CONTINUUM MECHANICS Victor Saouma Mechanics of Materials II Draft 6.4 Con...

Ngày tải lên: 13/08/2014, 17:20

... zero: (σ rr ) r=a =0 ✛ (9 .74 -a) (σ rθ ) r=a =0 ✛ (9 .74 -b) 59 Upon substitution in Eq. 9 .70 the four boundary conditions (Eq. 9 .73 -c, 9 .73 -d, 9 .74 -a, and 9 .74 -b) become −  2A + 6C b 4 + 4D b 2  = 1 2 σ 0 (9 .75 -a)  2A ... Strength of Materials yielding for this problem (carefull about the sign) σ rr = σ 0 2  1 − a 2 r 2  (9 .77 -a) σ θθ = σ 0 2  1+ a 2 r 2  (9 .77 -b)...

Ngày tải lên: 13/08/2014, 17:20

... .9851 .74 94 .74 94 .6262 1.25 1.2405 1.0168 .79 29 .79 29 . 670 1 1.30 1.24 57 1.0358 .8259 .8259 .70 53 1.40 1.2350 1.0536 . 872 3 . 872 3 .75 85 1.50 1.2134 1.0582 .9029 .9029 .79 71 1.60 1.1899 1.0 571 .9242 ... (11.30) Victor Saouma Mechanics of Materials II Draft 14 LEFM DESIGN EXAMPLES Victor Saouma Mechanics of Materials II Draft 12 LEFM DESIGN EXAMPLES M 1 =1.13 − 0....

Ngày tải lên: 13/08/2014, 17:20

... π 22 Figure 13 .7: Effect of Geometry and Load on Crack Stability, (Gdoutos 1993) Victor Saouma Mechanics of Materials II Draft 6 THEORETICAL STRENGTH of SOLIDS; (Griffith I) σ is the stress at the tip of the ... independent of the crack length. However, under plane stress R is found to be an increasing function of a, Fig. 13.9 59 If we examine an initial crack of length a i...

Ngày tải lên: 13/08/2014, 17:20