A Mixed Variational Principle of Fully Anisotropic Linear Elasticity

????? Sandhu ?? ?? ??? ????????? ????? ??? ???? ???? ???
??? ??? ?? ? ??? ???? ???????? ??????? (Mixed Variational P?lciple)
? ????. ???? ?? ƒÈtJ¿Õég?? self -adjoint ? ????????? ????? ??? ? ???
??? ? ?? ????? ? ??? ?? ??? ???? ???? £¬ ??? ?????? ??????
??? ? ?? ???? ? ?? (Consistency)? ?????? ????? ????? ????? ????
? ??. ? ??? ????? ?????? self - adjointness ??? ???? ????? ???? ??
?? ?????? ???? ??£¬ ??? ????? ?????? ??? ???????? ????
??? ? ??. ???? ??? ????? ? ? Reissner? ?? ??? ????? ??? ???
??? ??? ????? ?? ? ??? ??? ??????? ??? ? ?? ??? ??? ??.
? ??????? ? ???? ??? ? ???£¬ ???????? ?? ???£¬ ??? ????£¬ ??
???? ??? ?? ?? ?? ? ? ??

In this paper, a mixed variational principle applicable to the linear elasticity of inhom?'en¡Þus ??50-
tropic materials is presented. For derivation of the general variational principle, a systematic procedure
for the variational formulation of linear coupled boundary value problems developc'? by San?1u et ?.
is employed. Consistency condition of the field operators with the b¦Øndary 0?rators res?ts in explicit
inclusion of b¦Øndary conditions in the goveming functional. Extensions of admissible state function
spaces and specialization to a certain relation in the general goveming functional lead to the desir?
mixed variational principle. In the physical sense, the present variation? principle is analogous to the
Reissner¡¯s recent formulation obtain? by applying Lagrange multiplier technique followed by parti?
Legendre transform to the c1assical minimum potential energy principle. However, the present one is
more advantageous for the application to the general anisotropic materials since Reissner¡¯s principle
contains an irnplicit function which is not easily converted to an explicit form.