In this work, an efficient and robust isogeometric three-dimensional solid-beam finite element is developed for large deformations and finite rotations with merely displacements as degrees of freedom. The finite strain theory and hyperelastic constitutive models are considered and B-Spline and NURBS are employed for the finite element discretization. Similar to finite elements based on Lagrange polynomials, also NURBS-based formulations are affected by the non-physical phenomena of locking, which constrains the field variables and negatively impacts the solution accuracy and deteriorates convergence behavior. To avoid this problem within the context of a Solid-Beam formulation, the Assumed Natural Strain (ANS) method is applied to alleviate membrane and transversal shear locking and the Enhanced Assumed Strain (EAS) method against Poisson thickness locking. Furthermore, the Mixed Integration Point (MIP) method is employed to make the formulation more efficient and robust. The proposed novel isogeometric solid-beam element is tested on several single-patch and multi-patch benchmark problems, and it is validated against classical solid finite elements and isoparametric solid-beam elements. The results show that the proposed formulation can alleviate the locking effects and significantly improve the performance of the isogeometric solid-beam element. With the developed element, efficient and accurate predictions of mechanical properties of lattice-based structured materials can be achieved. The proposed solid-beam element inherits both the merits of solid elements e.g. flexible boundary conditions and of the beam elements i.e. higher computational efficiency.
The isogeometric boundary element algorithm for solving the plane strain problem of an elastic matrix containing an open material surface of arbitrary shape
University of Minnesota（明尼苏达大学）；Donghua University（东华大学）
Skew-symmetric Nitsche's formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact
Dalian University of Technology（大连理工大学）；University of Luxembourg（卢森堡大学）；Université Bourgogne Franche-Comté（勃艮第-弗朗什-孔泰大学）；Cardiff University（卡迪夫大学）；University of Western Australia（西澳大学）
A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling
SISSA-International School for Advanced Studies（国际高等研究院）；Technische Universität Braunschweig（布伦瑞克工业大学）；University of Pavia（帕维亚大学）；Technische Universität München（慕尼黑工业大学）
Convergence Analysis of Adaptive Finite Element Algorithms for a Regularized Variational Model of Quasi-Static Brittle Fracture in "Strain-Limiting" Elastic Solids
