美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）CQ9

Concept Question For the uniform state of plane strain shown in the fig ure,which one(s) of the following statement(s) is(are valid?(Assume Poisson's ratio v+0) 33≠0,∈11≠0,a2=0 ∈33≠0,∈11≠0,22=0 33≠0,∈11=0,622≠0 ≠0,∈11≠0,022≠0 Eqn. (1)and Eqn. 3) Cqn. (2)and Eqn. ( 3) Eqn. (4)and Eqn. (1) Eqn、(2) and Eqn.(4) DKDU

++++ ++++ ++++ ++++ ++++ Concept Question ++++ ++++ ++++ ++++ ++++ w δ L x x 1 3 d x x3 2 For the uniform state of plane strain shown in the fig￾ure, which one(s) of the following statement(s) is(are) valid? (Assume Poisson’s ratio ν �= 0): �33 �= 0, �11 �= 0, σ22 = 0 �33 �= 0, �11 �= 0,�22 = 0 �33 �= 0, �11 = 0,�22 �= 0 �33 �= 0, �11 �= 0, σ22 �= 0 1. ++++ Eqn.(1) and Eqn.(3) 2. ++++ Eqn.(2) and Eqn.(3) 3. ++++ Eqn.(4) and Eqn.(1) 4. ++++ Eqn.(2) and Eqn.(4) 5. ++++ DKDU (1) (2) (3) (4)

The only right answer is ·Eqn.(1) is wrong because o22≠0 due to poissons effect Eqn.(4)is correct, 633+0 due to the imposed displacement,∈1≠0 due to poisson' s effect and E22=0 because of the plane strain condition Eqn. 3) is wrong, it contradicts Eqn.(2) Eqn.(4) is correct, the plane strain conditions are actually materialized via u2=0

The only right answer is ++++ . • Eqn. (1) is wrong because σ22 �= 0 due to Poisson’s effect. • Eqn. (4) is correct, �33 �= 0 due to the imposed displacement, �11 �= 0 due to Poisson’s effect and �22 = 0 because of the plane strain condition. • Eqn. (3) is wrong, it contradicts Eqn. (2). • Eqn. (4) is correct, the plane strain conditions are actually materialized via u2 = 0