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

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.

Refined plate theory and its variants

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 137-146 ◽  
Author(s):  
R. P. Shimpi
Keyword(s):  
Plate Theory ◽  
Refined Plate Theory

Localization simulation of forming-induced residual stresses of composite using prescribed boundary

2021 ◽  
pp. 073168442094118
Author(s):  
Qi Wu ◽  
Hongzhou Zhai ◽  
Nobuhiro Yoshikawa ◽  
Tomotaka Ogasawara ◽  
Naoki Morita
Keyword(s):  
Residual Stresses ◽  
Representative Volume Element ◽  
Computational Cost ◽  
Volume Element ◽  
Thermoplastic Composite ◽  
Structural Deformation ◽  
Element Analysis ◽  
Micro Scale ◽  
Representative Volume ◽  
Localization Approach

A novel localization approach that seamlessly bridges the macro- and micro-scale models is proposed and used to model the forming-induced residual stresses within a representative volume element of a fiber reinforced composite. The approach uses a prescribed boundary that is theoretically deduced by integrating the asymptotic expansion of a composite and the equal strain transfer, thus rendering the simulation setting to be easier than conventional approaches. When the localization approach is used for the finite element analysis, the temperature and residual stresses within an ideal cubic representative volume element are precisely simulated, given a sandwiched thermoplastic composite is formed under one-side cooling condition. The simulation results, after being validated, show that the temperature gradient has an impact on the local residual stresses, especially on the in-plane normal stress transverse to the fiber, and consequently, influences the structural deformation. This newly designed localization approach demonstrates the advantages of enhanced precision and reduced computational cost owing to the fast modeling of the finely meshed representative volume element. This is beneficial for a detailed understanding of the actual residual stresses at the micro-scale.

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.

Dynamic Optimization of Steel Catenary Risers Based on Reliability Using Metamodel

2010 ◽  
Author(s):  
Wenqing Zheng ◽  
Hezhen Yang
Keyword(s):  
Dynamic Optimization ◽  
Computational Cost ◽  
Minimum Cost ◽  
Probabilistic Constraints ◽  
Optimization Approach ◽  
Element Analysis ◽  
Steel Catenary Riser ◽  
Reliability Based Design ◽  
Minimum Cost Design ◽  
Steel Catenary Risers

Reliability based design optimization (RBDO) of a steel catenary riser (SCR) using metamodel is investigated. The purpose of the optimization is to find the minimum-cost design subjecting to probabilistic constraints. To reduce the computational cost of the traditional double-loop RBDO, a single-loop RBDO approach is employed. The performance function is approximated by using metamodel to avoid time consuming finite element analysis during the dynamic optimization. The metamodel is constructed though design of experiments (DOE) sampling. In addition, the reliability assessment is carried out by Monte Carlo simulations. The result shows that the RBDO of SCR is a more rational optimization approach compared with traditional deterministic optimization, and using metamodel technique during the dynamic optimization process can significantly decrease the computational expense without sacrificing accuracy.

Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads

2005 ◽  
Vol 58 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Alan T. Zehnder ◽  
Mark J. Viz
Keyword(s):  
Fracture Mechanics ◽  
Plate Theory ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Crack Tip ◽  
Thin Plates ◽  
Element Analysis ◽  
Crack Tip Fields ◽  
Plates And Shells ◽  
Membrane Bending

The fracture mechanics of plates and shells under membrane, bending, twisting, and shearing loads are reviewed, starting with the crack tip fields for plane stress, Kirchhoff, and Reissner theories. The energy release rate for each of these theories is calculated and is used to determine the relation between the Kirchhoff and Reissner theories for thin plates. For thicker plates, this relationship is explored using three-dimensional finite element analysis. The validity of the application of two-dimensional (plate theory) solutions to actual three-dimensional objects is analyzed and discussed. Crack tip fields in plates undergoing large deflection are analyzed using von Ka´rma´n theory. Solutions for cracked shells are discussed as well. A number of computational methods for determining stress intensity factors in plates and shells are discussed. Applications of these computational approaches to aircraft structures are examined. The relatively few experimental studies of fracture in plates under bending and twisting loads are also reviewed. There are 101 references cited in this article.

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