Mixed-Dimensional Model Analysis Under Dimension Reduction Error Control

In order to conduct engineering analysis efficiently, complex CAD model is generally idealized by dimension reduction of its local thin regions into mid-surfaces, which results in a mixed-dimensional model. However, such dimension reduction inevitably induces analysis errors when plate or shell theory applied to the mixed-dimensional model.In this paper, an evaluation indicator is proposed for estimating analysis error induced by dimension reduction of a original model into mixed-dimensional model and used to control the analysis results of the mixed-dimensional model with given accuracy. The evaluation indicator is defined as the stress difference on the coupling interface between the mixed-dimensional model and the original model. When the mixed-dimensional model is analyzed, p-version solid elements were generated by offsetting the shell nodes in the thickness direction. Moreover, element stiffness matrix, boundary conditions and material properties can be extracted from the analysis results and reused for the indicator computation. Displacements of the mixed-dimensional model are input as initial value to iterative solver to accelerate the computation. When the indicator is below the accuracy, final analysis can be proceeded with p-adaptivity in the thin regions. The hierarchical shape function for p-version solid elements ensures the efficiency of the error estimation and the reliability of the final analysis. The robustness of the evaluation indicator and computational efficiency for final analysis are illustrated by experiments on engineering models.