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Item type:Publication, Access status: with files , Intrinsically selective mass scaling with hierarchic plate formulationsThe critical time step in explicit time integration methods depends on the highest natural angular frequency of the discretized problem. For shear deformable beam, plate and shell formulations, efficiency is therefore typically limited by the highest transverse shear frequencies, which are mostly of minor importance for the structural response. Direct parametrization using transverse shear variables within hierarchic structural element formulations allows a selective scaling of transverse shear frequencies in a simple manner, while bending frequencies remain practically unaffected. In particular, the novel concept of intrinsically selective mass scaling (ISMS) results in an efficient method that features high accuracy and preserves both linear and angular momentum for both consistent and lumped mass matrices. In addition, ISMS preserves the diagonal structure of lumped mass matrices. Similar to the underlying intrinsically locking-free, hierarchic concept for shear deformable structural element formulations, ISMS retains its beneficial properties for any smooth discretization scheme. In this contribution, we extend recent research on ISMS for beam formulations to the case of shear deformable plate formulations. We test our novel concept with respect to accuracy and efficiency by means of selected numerical experiments. We study both frequency spectra and the transient behavior in explicit time integration. To demonstrate the generality of ISMS, exemplarily both isogeometric discretizations based on B-splines and meshfree discretizations using local maximum-entropy approximants are investigated.Publicationtype: Journal Article31 50 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , An isogeometric Reissner–Mindlin shell element based on Bézier dual basis functions: Overcoming locking and improved coarse mesh accuracy(2020-10-01); ; ; ; We develop a mixed geometrically nonlinear isogeometric Reissner–Mindlin shell element for the analysis of thin-walled structures that leverages Bézier dual basis functions to address both shear and membrane locking and to improve the quality of computed stresses. The accuracy of computed solutions over coarse meshes, that have highly non-interpolatory control meshes, is achieved through the application of a continuous rotational approach. The starting point of the formulation is the modified Hellinger–Reissner variational principle with independent displacement, membrane, and shear strains as the unknown fields. To overcome locking, the strain variables are interpolated with lower-order spline bases while the variations of the strain variables are interpolated with the corresponding Bézier dual bases. Leveraging the orthogonality property of the Bézier dual basis, the strain variables are condensed out of the system with only a slight increase in the bandwidth of the resulting linear system. The condensed approach preserves the accuracy of the non-condensed mixed approach but with fewer degrees of freedom. From a practical point of view, since the Bézier dual basis is completely specified through Bézier extraction, any spline space that admits Bézier extraction can utilize the proposed approach directly.Publicationtype: Journal Article35 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization(2017-07-01); ; ; Two novel hierarchic finite element formulations for geometrically nonlinear shell analysis including the effects of transverse shear are presented. Both methods combine a fully nonlinear Kirchhoff–Love shell model with hierarchically added linearized transverse shear components. Thus, large rotations can be taken into account while circumventing the peculiar task of finding a corresponding parametrization of the rotation tensor. The two formulations differ in the way the transverse shear effects are included, either using hierarchic rotations or hierarchic displacements. The underlying assertion is that in most practical applications the transverse shear angles are small even for large deformations. This is confirmed by various numerical experiments. The hierarchic construction results in an additive strain decomposition into parts resulting from membrane and bending deformation and additional contributions from transverse shear. It requires at least C1-continuous shape functions, which can be easily established within the isogeometric context using spline based finite elements. As reported earlier, this concept is intrinsically free from transverse shear locking. In the nonlinear case it dramatically facilitates representation of large rotations in shell analysis.Publicationtype: Journal Article19