Balanced approximation spaces and mixed variational principles to eliminate locking effects in isogeometric shell analysis
平衡逼近空间和混合变分原理消除等几何壳分析中的锁定效应
基本信息
- 批准号:266714483
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Research Grants
- 财政年份:2014
- 资助国家:德国
- 起止时间:2013-12-31 至 2018-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Isogeometric finite element formulations aid and abet a tighter linkage between design and analysis. The geometry description of the design system together with its basis functions is used for analysis. Current CAD software is surface-oriented and uses NURBS (Non-Uniform Rational B-Splines) to describe the geometry. Thin-walled structures, e.g. free form surfaces, are defined merely by their reference surface using NURBS surfaces.The usage of NURBS in the context of the finite element method offers completely new possibilities. Besides geometry also spatial derivatives and the surface normal are defined exactly in every point for every discretization. Approximation spaces and their appropriate basis functions with the desired continuity between elements can be constructed by order elevation and knot insertion. The exact geometry is maintained. Considering these properties, an efficient, reliable and widely applicable isogeometric shell formulation for the analysis of thin-walled structures shall be developed. The geometry description of the CAD system shall be used as reference surface to define the shell body. Thus, an elaborate conversion into other geometry descriptions, e.g. NURBS volumes, can be avoided. The employed nonlinear kinematic shall allow large deformations and finite rotations. Transverse shear strains have to be considered. An exact description of the geometry in the thickness direction together with a consistent approximation of the kinematic is especially important to ensure convergence of deformations for order elevation. The computation of geometries with complex intersections shall require neither drilling rotation stabilization nor a manual intervention. Essential ingredients of an efficient and widely applicable shell formulation are efficacious methods for the elimination of locking effects as well as the incorporation of general three dimensional constitutive laws. The properties of NURBS shall be used advantageously to eliminate locking effects. Transverse shear locking is precluded by adapted approximation spaces with appropriate basis functions for deformations and rotations. A mixed variational formulation with independent deformations, strains and stresses significantly reduces membrane locking, as well as other locking effects. The choice of the solution spaces allows a statical condensation on element level to ensure numerical efficacy. An appropriate choice of the ansatz for strains and stresses allows the usage of general three dimensional constitutive laws without local iterations. Finally, a comprehensive set of benchmark examples shall be provided in order to show the capability of the proposed methods.
等几何有限元公式有助于并促使设计和分析之间的联系更加紧密。设计系统的几何描述及其基本功能用于分析。目前的CAD软件是面向曲面的,并使用NURBS(非均匀有理B样条)来描述几何形状。薄壁结构,例如自由曲面,仅通过NURBS曲面的参考曲面来定义。在有限元法中使用NURBS提供了全新的可能性。除了几何,空间导数和表面法线也被精确地定义在每个离散化的每个点上。近似空间及其相应的基函数可以通过阶提升和节点插入来构造。保持精确的几何形状。考虑到这些性质,一个有效的,可靠的和广泛适用的等几何壳公式的薄壁结构的分析应发展。应使用CAD系统的几何描述作为定义壳体的参考面。因此,可以避免到其他几何描述(例如NURBS体积)的复杂转换。所采用的非线性运动学应允许大变形和有限旋转。必须考虑横向剪切应变。在厚度方向上的几何形状的精确描述连同运动学的一致近似对于确保阶提升的变形的收敛特别重要。具有复杂相交的几何形状的计算既不需要钻孔旋转稳定,也不需要人工干预。一个有效的和广泛适用的壳配方的基本成分是有效的方法,消除锁定效应,以及一般的三维本构关系的纳入。应有利地利用NURBS的特性来消除锁定效应。横向剪切锁定是排除了适应近似空间与适当的基函数的变形和旋转。具有独立变形、应变和应力的混合变分公式显著减少了膜锁定以及其他锁定效应。选择的解决方案空间允许静态凝聚的元素水平,以确保数值效率。应变和应力的一个适当的选择的ANDERANT允许使用一般的三维本构关系,而无需局部迭代。最后,应提供一套全面的基准示例,以显示所提出的方法的能力。
项目成果
期刊论文数量(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Adjusted approximation spaces for the treatment of transverse shear locking in isogeometric Reissner–Mindlin shell analysis
- DOI:10.1016/j.cma.2019.05.037
- 发表时间:2019-09
- 期刊:
- 影响因子:7.2
- 作者:G. Kikis;W. Dornisch;S. Klinkel-
- 通讯作者:G. Kikis;W. Dornisch;S. Klinkel-
Separate control meshes for displacements and rotations for a shear locking free isogeometric Reissner‐Mindlin plate
用于无剪切锁定等几何 ReissnerâMindlin 板的位移和旋转的单独控制网格
- DOI:10.1002/pamm.201710129
- 发表时间:2017
- 期刊:
- 影响因子:0
- 作者:Kikis G.;Klinkel S.
- 通讯作者:Klinkel S.
Isogeometric Reissner‐Mindlin shell analysis ‐ employing different control meshes for displacements and rotations
- DOI:10.1002/pamm.201610093
- 发表时间:2016-10
- 期刊:
- 影响因子:0
- 作者:G. Kikis;W. Dornisch;Sven Klinkel-
- 通讯作者:G. Kikis;W. Dornisch;Sven Klinkel-
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Professor Dr.-Ing. Sven Klinkel其他文献
Professor Dr.-Ing. Sven Klinkel的其他文献
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{{ truncateString('Professor Dr.-Ing. Sven Klinkel', 18)}}的其他基金
A finite element model for the analysis of the nonlinear mechanical behavior of hybrid composite materials
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An adaptive FE²-model for the analysis of the non-linear, thermo-mechanically coupled behavior of fiber-matrix composites
用于分析纤维基复合材料的非线性热机械耦合行为的自适应 FE² 模型
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283581644 - 财政年份:2015
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Scaled boundary isogeometric analysis with advanced features for trimmed objects, higher order continuity, and structural dynamics
缩放边界等几何分析,具有修剪对象、高阶连续性和结构动力学的高级功能
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285973342 - 财政年份:2015
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Using finite strain 3D-material models in beam and shell elements. An interface between arbitrary 3D-material laws and finite elements which include special stress conditions
在梁和壳单元中使用有限应变 3D 材料模型。
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5320194 - 财政年份:2001
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Naturally grown timber elements as basis for load-bearing building structures - structural analysis and growth simulation
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