Abstract
The technique has been presented for time-dependence identification of several independent beetwen each other loads distributed over a given area of a structure with arbitrary topology by using quantity values more convenient for measurements. In the assumption that the structure’s response linearly depends on the loads, the considered problem, which belongs to the class of boundary inverse problems in the mechanics of solids, is reduced to a system of linear algebraic equations for coefficients that approximate the sought-for influences. The system is solved using a regularizing algorithm providing stability of results to random errors in initial data and calculation errors. Concrete calculations, substantiating the efficiency of the presented technique, have been performed as with theoretical data to identify two non-stationary loads applied to a wheel carrier of a race car as with experimental data to restore an impact force applied to a round plate with fixed boundary. To calculate values of a system’s elements corresponding to values of measured quantities under unit loads, the finite element method was used. The suggested technique can be used for designing structures with complex geometry based on criterias of their dynamic (fatigue) strength, etc.
Highlights
The development of modern technology is inseparably linked to the design of new structures and improvement of existed ones, which should satisfy a required set of mechanical properties
There are many situations when this approach is difficult to implement or requires modification the structure under investigation. This substantially reduces the measurement accuracy. This problem can be solved using the technique of indirect measurements when sought-for loads are restored by registering more accessible measurement quantities associated with the loads
Restoring of external loads by their indirect manifestations relates to the “boundary inverse problem” in the mechanics of solids
Summary
The development of modern technology is inseparably linked to the design of new structures and improvement of existed ones, which should satisfy a required set of mechanical properties. The approaches developed so far for identifying external loads, which are based on numerical methods, and FEM in particular, assume the construction of so-called influence functions (coefficients) by solving one or a series of direct auxiliary problems for subsequent identification This approach is outlined in [8, 23, 24] for an approximate recovering the spatial distribution of quasi-static and time-periodic loads and given in [18] for approximate restoring of external loads represented as a set of concentrated forces. This paper is devoted to effective and based on the FEM method of inverse boundary problems solving for identification of dynamic external mechanical (quasi-static and non-stationary) loads acting on a structure with arbitrary geometry. These functions show the dynamics of some deformation parameter by action of sought-for loads, and they can be measured with appropriate sensors
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