The Tensor Measurement Of The Manifold And Its Application In The Engineering Strain Measurement

In engineering, the configuration of the object or its traces formed during its motion is an evolution manifold in the space. If the manifold can be measured from time to time, then the evolution of the manifold can be monitored, and after the corresponding mechanical and physical analysis about the procession of the evolution, the evolution law of the object can be got; hence such a kind of technology can be used to solve some related engineering problem. In the manufacture engineering, especially the top manufacture industry, they eagerly want to know the structure of the material and the hiding information about the structure, so the task of the macro measurement should also be one task of the engineering measurement. This research starts from geometry field theory(co-moving coordinate and gauge base vector), uses two kinds of theories including Chen Rational Mechanics and Clifford geometry algebra to measure the evolution of manifold, firstly establishing the general measure theory and method of the one-dimensional evolution manifold; then using it in the macro measurement, to get the strain measurement of one-dimensional manifold material; finally forming the measure theory and method for the material under some certain loading, and obtaining the strain figures through the measurement.Therefore, the research supplies the basis for the past mechanical state of the material. So, through this research give a rational answer about the fatigue-fracture problem. It also shows a new way to solve the problem in the manufracture.