Abstract:The fundamental mechanical equations were studied under the mechanical space. The differential stress operator and strain operator were obtained. There were strain energy operator and Hamilton operator for elastic body in same way, and the following results were testified. 1) The equilibrium equation of force is equivalent to the harmony equation of deformation under the mechanical space. They are all the basic mode of eigen equation of stress or strain operator. 2)
The eigen value of stress or strain operator is corresponding to the order of kinetic energy of elastic body, and the elastic wave represents the non-basic mode. 3) The eigen functions of stress operator or strain operator corresponding to some kinetic energy order are fields of modal stress or modal strain in same order. 4) The eigen equations of strain energy operator are the fundamental equations of elastic mechanics which are expressed with the potential functions.

Key words: anisotropic solid; elastic mechanics; mechanical operator; operationalized principle