Cosserat理论的应变能定理及解的唯一性

Cosserat理论已广泛应用于岩土工程，求解Cosserat问题时，解析方法与数值方法都曾被采用，证明了Cosserat问题的能量原理及解的唯一性定理，进一步完善了该理论，并保证了数值及解析求解结果的正确性。

STRAIN ENERGY THEOREM OF COSSERAT THEORY AND UNIQUENESS OF ITS SOLUTION

Cosserat continuum theory has been applied widely in geotechnical engineering and other fields,such as composites mechanics,biological mechanics. When dealing with engineering problems with Cosserat Theory,both analytic and numerical methods have been adopted in analysis process. As the solutions obtained with different methods appears with differently forms,the uniqueness of solution is needed to be verified to ensure the results achieved are the answer to problems exactly no matter how different the expressions look from each other and both analytic and numerical methods are effective. Though the number of Cosserat stresses and strains components are more then conditional continuum theory,it has been proved that work done on the Cosserat elastic body is equate to the strain energy gained by the body if no energy dissipated during loading. Moreover,the theorem of uniqueness of solution for Cosserat theory has been proved in this paper,and it provids warrant for the adoption of different analysis methods. Finally,the problem of stress concentration around small hole in plate is analyzed with Cosserat theory by adopting both analytic and numerical methods,and the results are compared and identical with each other.