美国麻省理工大学：结构分析与设计技术：CQ9

++++ ++++ ++++ ++++ ++++ Concept Question ++++ ++++ ++++ ++++ ++++ w δ L x x 1 3 d x x3 2 For the uniform state of plane strain shown in the ?g- ure, which one(s) of the following statement(s) is(are) valid? (Assume Poisson’s ratio ν ?= 0): ? 33 ?= 0, ? 11 ?= 0,σ 22 = 0 ? 33 ?= 0, ? 11 ?= 0,? 22 = 0 ? 33 ?= 0, ? 11 = 0,? 22 ?= 0 ? 33 ?= 0, ? 11 ?= 0,σ 22 ?= 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 σ 22 ?= 0 due to Poisson’s e?ect. ? Eqn. (4) is correct, ? 33 ?= 0 due to the imposed displacement, ? 11 ?= 0 due to Poisson’s e?ect 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 u 2 = 0.