关键词: stochastic process, threshold-crossing, statistical property

Abstract: A Solution of elastostatic problem is defined on the basis of set theory and extended to the cases with fuzzy boundary conditions. Extension is also given for the principles of minimum potential energy and minimum complementary work with fuzzy boundary conditions. A quasisolution of an elastostatic problem is defined as an approximate solution with boundary conditions most close to the original. And the existance of quasisolution of an elastostatic problem can be proved on the basis of certain assumptions and the theorem of minimum elementary potential energy.

Key words: stochastic process, threshold-crossing, statistical property