Theory and numerics of layered shells with variationally embedded interlaminar stresses

Present paper deals with layered shells subjected to static loading. The basic equations include besides the global equilibrium formulated in terms of stress resultants, the local equilibrium in terms of stresses, the geometric field equations, the constitutive equations, a constraint which enforces the correct shape of the superposed displacement field through the thickness and the boundary conditions. Thereby an interface to three-dimensional material laws is created. The weak form of the boundary value problem is derived and a finite element formulation for quadrilaterals is specified. The mixed hybrid shell element possesses the usual 5 or 6 nodal degrees of freedom. This allows standard geometrical boundary conditions and the elements are applicable also to shell intersection problems. For linear elasticity the computed transverse shear stresses are automatically continuous at layer boundaries and zero at the outer surfaces. In comparison to fully 3D computations present element formulation needs only a fractional amount of computing time. •An interface to 3D material models is available.•For linear elasticity there is automatically continuity of the interlaminar shear stresses.•Use of standard nodal degrees of freedom allows computation of shell intersection problems.•Present model requires only a fractional amount of computing time in comparison with fully 3D computations.