Dimensional Reduction in Elasticity Using a Variational Perturbation Approach

초록

Dimensional reduction in elastic analyses is conventionally achieved through kinematic assumptions in classical beam theories; however, these assumptions can produce constitutive relationships with limited mathematical clarity. To overcome this limitation, this study introduces a variational perturbation approach for dimensional reduction, which incorporates perturbation displacements orthogonal to an assumed displacement field. This method allows the derivation of reduced-order constitutive equations directly from three-dimensional elasticity, without relying on plane-stress assumptions. The formulation is applied to classical beam theory, first-order shear deformation theory, and higher-order beam theories. The accuracy and validity of the reduced models are evaluated through conservation-law analyses based on Noether's theorem and by assessing shear correction factors.

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