There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational princip...There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain?This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics.This investigation finds that as long as the functional has one of the combinations(A(ε_(ij))-σ_(ij)ε_(ij))or(B(σ_(ij))-σ_(ij)ε_(ij)),its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method.This research proves that the Hu-Washizu functionalΠ(u_(ij),ε_(ij),σ_(ij))is real three-field functional,and resolves the historic academic controversy on the issue of constructing a three-field functional.展开更多
基金Project supported by Xi’an University of Architecture and Technology(No.002/2040221134)。
文摘There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain?This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics.This investigation finds that as long as the functional has one of the combinations(A(ε_(ij))-σ_(ij)ε_(ij))or(B(σ_(ij))-σ_(ij)ε_(ij)),its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method.This research proves that the Hu-Washizu functionalΠ(u_(ij),ε_(ij),σ_(ij))is real three-field functional,and resolves the historic academic controversy on the issue of constructing a three-field functional.
