Displacement–strain transformation for a variable cross-section beam based on hypergeometric and Meijer-G functions

The modal-learning displacement–strain transformation has been proved to be able to predict the strain of the typical uniform beam. However, as the complexity of the structure increases, for example, the shape of the beam cross-section changes. The typical displacement–strain transformation is no longer applicable due to the unknown mode function. To further explore this issue, the hypergeometric and Meijer-G functions are used to establish the mode shape function with good structural adaptability. A displacement–strain transformation method based on the hypergeometric and Meijer-G functions is proposed to predict the dynamic strain of the variable cross-section beam. Experiment results demonstrate that the proposed method can solve the problem of full-field strain prediction for beams with variable sections and boost the displacement–strain transformation’s theoretical calculation accuracy. Under sinusoidal excitation and random excitation, the strain prediction accuracy reaches 99.69% and 99.25%, respectively. This approach simplifies the preprocessing of the structure, and provides a welcome boost to developing the displacement–strain transformation method in full-field strain measurement. •A displacement-strain transformation method is proposed to predict the full-field dynamic strain of variable cross-section beams.•The mode function of the variable cross-section beam with good structural adaptability is established.