<p>Based on nonlocal elasticity theory, this paper explores the explicit surface stress-deformation relationship in bending rectangular microcantilevers to reveal micro-nano nonlocal effects. Integrating nonlocal elasticity and Euler-Bernoulli beam theories, this paper derived a variable-coefficient differential-integral governing equation under uniform surface stress assumption, solved via Taylor series expansion to get explicit relationship of deformation and surface stress. Numerical examples verify the model’s accuracy by comparing with the model results in the literature, verify the convergence of the method by comparing zero-, second-, and fourth-order expansions, and analyze the impact of size parameters on microbeam static deformation. Results show nonlocal theory—via dimensionless size parameter—can better predict bending deformation than classical theory, especially as dimensions approach material length scales. This explicit relationship provides theoretical support for the design/optimization of microbeam sensors and micro-nano sensor technologies, and future research can be extended to other microcantilever shapes/structures.</p>

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Bending analysis of microcantilever surface stress sensors based on nonlocal elasticity theory

  • Jin Wu,
  • Yao Zhang,
  • Zhebin Pan,
  • Bin Tan,
  • Yirui Yang,
  • Yang Chen,
  • Xulong Peng

摘要

Based on nonlocal elasticity theory, this paper explores the explicit surface stress-deformation relationship in bending rectangular microcantilevers to reveal micro-nano nonlocal effects. Integrating nonlocal elasticity and Euler-Bernoulli beam theories, this paper derived a variable-coefficient differential-integral governing equation under uniform surface stress assumption, solved via Taylor series expansion to get explicit relationship of deformation and surface stress. Numerical examples verify the model’s accuracy by comparing with the model results in the literature, verify the convergence of the method by comparing zero-, second-, and fourth-order expansions, and analyze the impact of size parameters on microbeam static deformation. Results show nonlocal theory—via dimensionless size parameter—can better predict bending deformation than classical theory, especially as dimensions approach material length scales. This explicit relationship provides theoretical support for the design/optimization of microbeam sensors and micro-nano sensor technologies, and future research can be extended to other microcantilever shapes/structures.