A New Plate Formulation Based on Triangular Isogeometric Analysis

2018 ◽  
Author(s):  
Mehrdad Zareh ◽  
Xiaoping Qian
Keyword(s):  
Convergence Rate ◽  
Isogeometric Analysis ◽  
Complex Geometry ◽  
Plate Theory ◽  
Necessary Condition ◽  
Local Refinement ◽  
Geometric Models ◽  
Plate Elements ◽  
Element Technique ◽  
C1 Continuity

This paper presents application of rational triangular Bezier splines (rTBS) for developing Kirchhoff-Love plate elements in the context of isogeometric analysis. Triangular isogeometric analysis can provide the C1 continuity over the mesh including elements interfaces, a necessary condition in finite elements formulation based on Kirchhoff-Love shell and plate theory. Using rTBS and macro-element technique, we develop Kirchhoff-Love plate elements, investigate the convergence rate and apply the method on complex geometry. Obtained results demonstrate that the optimal convergence rate is achievable; moreover, this method is applicable to represent thin geometric models of complex topology or thin geometric models in which efficient local refinement is required.

Static analysis of FG plates using T-splines based isogeometric approach and a refined plate theory

2020 ◽  
pp. 002199832096771
Author(s):  
Zhenyu Liu ◽  
Chuang Wang ◽  
Guifang Duan ◽  
Jianrong Tan
Keyword(s):  
Static Analysis ◽  
Plate Theory ◽  
Computational Cost ◽  
Control Points ◽  
Local Refinement ◽  
Element Analysis ◽  
Refined Plate Theory ◽  
Fg Plates ◽  
Shear Deformation Theories ◽  
C1 Continuity

In this study, a novel refined plate theory (RPT) is developed for the geometrically linear static analysis of FG plates, which is a simplification of the higher-order shear deformation theories (HSDTs). It improves the computational efficiency while preserving the accuracy advantage of HSDTs. The C1-continuity problem is overcome by isogeometric analysis (IGA), which shows more advantages than the C0 elements based finite element analysis. By T-splines, the computational cost is effectively reduced, since compared to NURBS based IGA, T-splines can achieve local refinement and improve the utilization of control points. The rule of mixture with power-law and Mori–Tanaka scheme are adopted to calculate the material properties of the plate. Several numerical experiments are given to prove the efficiency of the proposed method

Delamination of Laminate Plates

2014 ◽  
Vol 969 ◽  
pp. 97-100 ◽  
Author(s):  
Eva Kormaníková
Keyword(s):  
Finite Element Analysis ◽  
Mixed Mode ◽  
Plate Theory ◽  
Laminate Plate ◽  
Element Analysis ◽  
Interface Elements ◽  
First Order ◽  
Plate Elements ◽  
Interface Modeling ◽  
Shear Deformable

The paper deals with numerical modeling of delamination of laminate plate consists of unidirectional fiber reinforced layers. The methodology adopts the first-order shear laminate plate theory and fracture and contact mechanics. There are described sublaminate modeling and delamination modeling by the help of finite element analysis. With the interface modeling there is calculated the energy release rate along the lamination front. Numerical results are given for mixed mode delamination problems by implementing the method in a 2D finite analysis, which utilizes shear deformable plate elements and interface elements. Numerical example is done by the commercial ANSYS code.

Implicit Boundary Approach for Reissner-Mindlin Plates

2013 ◽  
Author(s):  
Hailong Chen ◽  
Ashok V. Kumar
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Weak Form ◽  
Mindlin Plate ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Boundary Method ◽  
Solid Models ◽  
Plate Elements ◽  
Background Mesh

Implicit boundary method enables the use of background mesh to perform finite element analysis while using solid models to represent the geometry. This approach has been used in the past to model 2D and 3D structures. Thin plate or shell-like structures are more challenging to model. In this paper, the implicit boundary method is shown to be effective for plate elements modeled using Reissner-Mindlin plate theory. This plate element uses a mixed formulation and discrete collocation of shear stress field to avoid shear locking. The trial and test functions are constructed by utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied. The incompatibility of discrete collocation with implicit boundary approach is overcome by using irreducible weak form for computing the stiffness associated with essential boundary conditions. A family of Reissner-Mindlin plate elements is presented and evaluated in this paper using several benchmark problems to test their validity and robustness.

UV-Activated Frequency Control of Beams and Plates Based on Isogeometric Analysis

2017 ◽  
Author(s):  
Yujie Guo ◽  
Hornsen Tzou
Keyword(s):  
Isogeometric Analysis ◽  
Uv Light ◽  
Frequency Control ◽  
Dynamic Stiffness ◽  
Frequency Variation ◽  
Frequency Change ◽  
Engineering Structures ◽  
Plate Structures ◽  
C1 Continuity ◽  
Euler Bernoulli Beam

A new LaSMP smart material exhibits shape memory behaviors and stiffness variation via UV light exposures. This dynamic stiffness provides a new noncontact actuation mechanism for engineering structures. Isogeometric analysis utilizes high order and high continuity NURBS as basis functions which naturally fulfills C1-continuity requirement of Euler-Bernoulli beam and Kirchhoff plate theories. The UV light-activated frequency control of LaSMP laminated beam and plate structures based on the isogeometric analysis is presented in this study. The accuracy and efficiency of the proposed isogeometric approach are demonstrated via several numerical examples in frequency control. The results show that, with LaSMPs, broadband frequency control of beam and plate structures can be realized. Furthermore, the length of LaSMP patches on beams is varied, which further broadens its frequency variation ranges. Studies suggest that 1) the newly developed IGA is an effective numerical tool and 2) the maximum frequency change ratio of beam and plate structures respectively reach 24.30% and 6.37%, which demonstrates the feasibility of LaSMPs induced vibration control of structures.

Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element

1981 ◽  
Vol 48 (3) ◽  
pp. 587-596 ◽  
Author(s):  
T. J. R. Hughes ◽  
T. E. Tezduyar
Keyword(s):  
Finite Elements ◽  
Good Accuracy ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Isoparametric Element ◽  
Practical Applications ◽  
Plate Elements ◽  
Mindlin Plate Theory

Concepts useful for the development of Mindlin plate elements are explored. Interpolatory schemes and nodal patterns which are ideal according to the proposed criteria are found to be somewhat more complicated than desirable for practical applications. However, these ideas are found to be useful as starting points in the development of simpler elements. This is illustrated by the derivation of a new four-node bilinear quadrilateral which achieves good accuracy without ostensible defect.

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