MindlinReissnerSchalenelemente

Mindlin-Reissner shell elements are specialized finite elements used in computational mechanics to model thin to moderately thick shells and plates. They are designed to address the limitations of classical thin-shell theories, such as those based on Kirchhoff-Love assumptions, which neglect transverse shear deformation and rotary inertia effects. These approximations can lead to inaccuracies in analyzing structures with significant thickness or under high-frequency dynamic loading.

The Mindlin-Reissner theory, also known as the first-order shear deformation theory (FSDT), introduces additional degrees of freedom to account for transverse shear strains and rotary inertia. In contrast to Kirchhoff-Love elements, which typically use only three displacement degrees of freedom (axial, transverse, and rotational), Mindlin-Reissner elements incorporate an additional rotational degree of freedom at each node, often resulting in six degrees of freedom per node (three displacements and three rotations). This enhancement improves accuracy for thicker shells and dynamic problems.

Mindlin-Reissner shell elements are widely employed in finite element analysis (FEA) software to simulate structures like aircraft wings, pressure vessels, and automotive components. Their ability to capture shear deformation and rotary inertia makes them particularly useful for nonlinear analyses, impact simulations, and high-frequency vibrations. However, they may require shear correction factors to account for the overestimation of shear stiffness inherent in the theory.

These elements are often implemented in quadrilateral or triangular formulations, with various interpolation schemes for the displacement and rotational fields. Common variants include the Mindlin-Reissner-Reissner-Mindlin (MRRM) elements, which further refine the formulation for improved accuracy. While computationally more expensive than thin-shell elements, Mindlin-Reissner shell elements provide a robust balance between accuracy and efficiency for a broad range of engineering applications.