Finite Element Method Based On Interval Mathematics And Its Study Of The Engineering Application

When taking the engineering problems as some mechanical model, some uncertain mechanical factors can be likely to be contacted, such as mechanical parameters of engineering structures. The deviser often cares about when some parameters vary in certain scope, the reflection range of the structure need to be known in order to assure its carrying capacity. If the uncertain factors can be denoted by relative interval variable, which can be limited by certain interval, the finite element method can be connected with the interval mathematics, and then the interval finite element method can be created. Be based on reading lots of correlative articles of inland and overseas, the paper's central contents indicate as follows.Firstly, In the face of the solving to control equation of the static interval finite element method, the paper brings one method, which is dividing the interval parameters into some small subintervals, when the interval parameters changes in large scope, and then compile the relevant programs. The other is dividing the element interval stiffness matrixes into some small subintervals. Both of them are written relevant mathematic expression, which are based on the interval finite element method, which is based on elements, and then compile the relevant programs. Through the examples, comparing it with other methods, the results indicate that the method brought by this paper is reasonable.Secondly, In the face of structures' self-quivering in dynamic interval finite element method, for the solving problem about structures' inherent frequency, the paper brings the optimization method, and for the quiver shape, using the interval perturbation method and compiling the relevant programs in virtue of large mathematic software MATLAB.At last, compare the static interval finite element method based on interval parameters' subintervals perturbation method with the certain finite element method in some underground engineering, the results indicate the static interval finite element method based on interval parameters' subintervals perturbation method brought by the paper is feasible.