Strain determination on arbitrarily oriented planes

Abstract

Strain gauge methods are widely used in the testing of specimens and elements of aircraft structures to assess the local stress-strain state (SSS) experimentally. These methods provide critical information about the SSS at specific points, which is essential for determining the structure’s strength and reliability. During full-scale strain measurements, the magnitudes and directions of strains on planes oriented at arbitrary angles must be determined. This is especially important when analyzing complex loading conditions or when the orientation of structural elements does not coincide with the coordinate system in which measurements are performed. Additional difficulties occur when an element of a strain gauge rosette fails, making it impossible to apply traditional methods for determining strain components. This paper proposes an alternative approach based on the use of three individually placed but maximally grouped strain gauges arranged at arbitrary angles relative to each other or relative to the strain rosette’s working elements. The methodology for determining strain components on arbitrarily oriented planes is described in detail, including mathematical relationships that connect the geometric arrangement of measuring elements with the resulting strain values. Experimental and numerical techniques are proposed to evaluate the SSS on arbitrary planes, particularly the finite element method (FEM), which allows for the modeling of complex deformation states and accurate calculations under real operational loads. The analysis confirmed the high accuracy of the proposed approach and demonstrated consistency between analytical solutions, experimental data, and numerical results. The use of three maximally grouped separate strain gauges significantly expands the capabilities of strain gauge measurements, making them effective even in complex cases where traditional techniques are no longer applicable. The obtained results may be useful for further development of experimental methods for evaluating the SSS and their application in the aerospace industry.