美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）CQ10

Concept Question How can the paradox with the spring be plained? In other words, which of the following statements is true 1. Equilibrium can be derived from the equiv alence of the external and the internal work 2. Equilibrium is an artifact of our imagina- tion 3. Equilibrium only considers the final state and not the process by which it has been reached. Intermediate states are ignored and may violate equilibrium 4. Equilibrium can be derived from the mini mization of potential en Statements(3)and(4) 2 Statements(1)and all of the above 4. None of the above DKDU

++++ ++++ ++++ ++++ ++++ Concept Question ++++ ++++ ++++ ++++ ++++ How can the paradox with the spring be ex￾plained ? In other words, which of the following statements is true? 1. Equilibrium can be derived from the equiv￾alence of the external and the internal work. 2. Equilibrium is an artifact of our imagina￾tion. 3. Equilibrium only considers the final state and not the process by which it has been reached. Intermediate states are ignored and may violate equilibrium. 4. Equilibrium can be derived from the mini￾mization of potential energy. 1. ++++ Statements (3) and (4). 2. ++++ Statements (1) and (2). 3. ++++ All of the above. 4. ++++ None of the above. 5. ++++ DKDU

The right answer is(1) ●Eqn.(??) is wrong because o22≠0 due to Poisson’ s effect Eqn.(?? )is correct, 633+0 due to the mposed displacement,∈11≠0 due to pois sons effect and E22=0 because of the plane strain condition Eqn.(?? ) is wrong, it contradicts Eqn. (??) Eqn.(?? ) is correct, the plane strain condi tions are actually materialized via u?=0

The right answer is (1) ++++ . • Eqn. (??) is wrong because σ22 6= 0 due to Poisson’s effect. • Eqn. (??) is correct, �33 6= 0 due to the imposed displacement, �11 6= 0 due to Pois￾son’s effect and �22 = 0 because of the plane strain condition. • Eqn. (??) is wrong, it contradicts Eqn. (??). • Eqn. (??) is correct, the plane strain condi￾tions are actually materialized via u2 = 0