The corotational method for frame-invariant elements is generalized to obtain a consistent large-strain shell element incorporating thickness extensibility. The resulting element allows arbitrary in-plane deformations and is distinct from the traditional corotational methods (either quadrature-based or element-based) in the sense that the corotational frame is exact. The polar decomposition operation is performed in two parts, greatly simplifying the linearization calculations. Expressions for the strain-degreesof-freedom matrices are given for the first time. The symbolic calculations are performed with a well-known algebraic system with a code generation package. Classical linear benchmarks are shown with excellent results. Applications with hyperelasticity and finite strain plasticity are presented, with asymptotically quadratic convergence and very good benchmark results. An example of finite strain plasticity with fracture is solved successfully, showing remarkable robustness without the need of enrichment techniques.

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Highlights• Finite strain solid-shell element with good distortion insensitivity.• Shell benchmarking and comparison with established techniques.• Motion of anisotropic axes by use of Lowdin frames.• Constitutive framework based on a consistent updated-Lagrangian formulation with smoothed complementarity condition.• Combination with standard 3D elements avoids additional tasks. AbstractA finite-strain solid-shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-ofreference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhancedassumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

This work presents a methodology to assess maintenance teams in the determination of the degree of redundancy that an active component must have in order to minimize its system life-cycle cost and in the definition of the corresponding maintenance plan schedule. The minimal required data are three average costs and one reliability function. It is useful in a system's design phase, since in this situation data is usually scarce or inaccurate, but can also be applied in the exploration phase. It is an adaptation of the classical Optimal Age Replacement method combined with a redundancy allocation problem. A set of simple illustrative examples covering a variety of operating conditions is presented, demonstrating quantitatively the applicability to a range of maintenance optimization decisions.