Kirchhoff–Love shells within strain gradient elasticity: Weak and strong formulations and an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml31" display="inline" overflow="scroll" altimg="si31.gif"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>-conforming isogeometric implementation

A strain gradient elasticity model for shells of arbitrary geometry is derived for the first time. The Kirchhoff–Love shell kinematics is employed in the context of a one-parameter modification of Mindlin’s strain gradient elasticity theory. The weak form of the static boundary value problem of the generalized shell model is formulated within an H3 Sobolev space setting incorporating first-, second- and third-order derivatives of the...