A Modified Strain-displacement Method for High Accuracy 8-Node Solid Finite Element

2020 ◽  
Author(s):  
Sacharuck Pornpeerakeat ◽  
Krissachai Sriboonma ◽  
Arisara Chaikittiratana
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Higher Order ◽  
Curvilinear Coordinates ◽  
Computational Time ◽  
Element Formulation ◽  
Displacement Method ◽  
Energy Equivalence ◽  
Computational Resources ◽  
Locking Phenomena

Higher-order three-dimensional solid elements are widely used for machine design and structural analyses. Although higher-order solid elements offer higher accuracy, the assembly routines often consume large amount of computational time and memory usage. In contrast, lower-order solid elements such as an 8-nod are simpler in programming implementation and consume less computational resources. However, they can produce problems of locking phenomena e.g. membrane and shear locking. Moreover, in a three-dimensional analysis using continuum solid elements, it is necessary to consider the stresses in the through-thickness direction, for example, in layered soil and foundation. This research aims to develop a modified strain-displacement finite element formulation that eliminates locking problems and generally applicable to both thick and thin threedimensional structures. The proposed formulation is based on the key concept of energy equivalence mapped between the global and natural curvilinear coordinates. The advantage of the proposed method is the ability to select a set of chosen strain functions that can be defined arbitrarily on the natural curvilinear coordinates.

Three-dimensional pulse response of curved composite sandwich panel with compressible core using non-linear higher-order theory

2020 ◽  
pp. 109963622098008
Author(s):  
Seyed Ali Ahmadi ◽  
Mohammad Hadi Pashaei ◽  
Ramazan-Ali Jafari-Talookolaei
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Sandwich Panel ◽  
Viscoelastic Model ◽  
Three Dimensional ◽  
Higher Order ◽  
Computer Hardware ◽  
Computational Time ◽  
Damping Factor ◽  
Non Linear

In this paper, the dynamic response of cylindrical sandwich panels with compressible core is obtained using the extended non-linear higher-order sandwich panel theory. It is assumed that the sandwich panel has simply supported boundary at all edges and is consisted of orthotropic face sheets and viscoelastic core layer. To describe the mechanical properties of the viscoelastic foam core, the Kelvin-Voigt linear viscoelastic model was applied. Three-dimensional linear equations of motions were used to describe the sandwich panel deformations. The effects of various parameters including the panel span, core and facing thickness, the viscous damping factor, pulse duration, and maximum pressure on the dynamic response of the sandwich cylindrical panel are studied. The results obtained from present method are compared with finite element solutions and those reported in the literature, and consequently, agreement among the results could be observed. The results shown that applied viscoelastic model has a signification effect on the panel response and reduces the magnitude of vibrations. The presented programming code (DQ) needs less computational time and computer hardware capacity and is faster than finite element solution.

Stability of Layered Structures with Hybridized Configuration by Means of a Reddy-Type Higher-Order Finite Element Formulation

2021 ◽  
pp. 2150045
Author(s):  
Zhen Wu ◽  
Jie Zhou ◽  
Zhengliang Liu ◽  
Rui Ma ◽  
Xiaohui Ren
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Three Dimensional ◽  
Middle Surface ◽  
Layered Structures ◽  
Higher Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Buckling Loads ◽  
Proposed Model

To make use of the merit of designability, each lamina in layered structures may possess diverse materials and geometry to realize specific application. For the hybridized structures, geometry and material properties relative to the middle surface are generally unsymmetrical, which have a significant impact on stability. Some models might lose capability to deal with such issues, so that these issues are less reported. Within the developed models, Reddy’s model possesses merit of simplicity and efficiency, so a Reddy-type higher-order zig-zag model is constructed by utilizing the proposed zig-zag function (ZZF). Instead of the standard finite element formulation using the principle of minimum potential energy, the three-field Hu–Washizu (HW) mixed variational principle is employed to acquire the finite element formulation which can meet the harmonious conditions of transverse shear stress at the interface of adjacent layers. By investigating buckling behaviors of hybridized structures, performance of the proposed finite element formulation is appraised by comparing with the results obtained from the three-dimensional (3D) model as well as other models. Effect of boundary conditions (BCs), material properties, and span-to-thickness ratio on the buckling loads is also studied in detail. Numerical results show that buckling loads of hybridized structures are significantly impacted by the chosen parameters. The results acquired from proposed model are in very good agreement with those obtained from the layerwise (LW) model and the 3D finite element results.

scholarly journals Polygonal finite elements for three-dimensional Voronoi-cell-based discretisations

2012 ◽  
Author(s):  
Kaliappan Jayabal ◽  
Andreas Menzel
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Three Dimensional ◽  
Specific Property ◽  
Voronoi Cell ◽  
Polycrystalline Materials ◽  
Element Formulation ◽  
Hybrid Finite Element ◽  
Grain Structures ◽  
Polygonal Elements

Hybrid finite element formulations in combination with Voronoi-cell-based discretisation methods can efficiently be used to model the behaviour of polycrystalline materials. Randomly generated three-dimensional Voronoi polygonal elements with varying numbers of surfaces and corners in general better approximate the geometry of polycrystalline microor rather grain-structures than the standard tetrahedral and hexahedral finite elements. In this work, the application of a polygonal finite element formulation to three-dimensional elastomechanical problems is elaborated with special emphasis on the numerical implementation of the method and the construction of the element stiffness matrix. A specific property of Voronoi-based discretisations in combination with a hybrid finite element approach is investigated. The applicability of the framework established is demonstrated by means of representative numerical examples.

Higher-Order Plate Elements for Large Deformation Analysis in Multibody Applications

2016 ◽  
Author(s):  
Henrik Ebel ◽  
Marko K. Matikainen ◽  
Vesa-Ville Hurskainen ◽  
Aki Mikkola
Keyword(s):  
Large Deformation ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Higher Order ◽  
Deformation Analysis ◽  
Numerical Convergence ◽  
Plate Elements ◽  
Negative Effect ◽  
Numerical Performance ◽  
Locking Phenomena

This study introduces higher-order three-dimensional plate elements based on the absolute nodal coordinate formulation (ANCF) for large deformation multibody applications. The introduced elements employ four to eight nodes and the St. Venant-Kirchhoff material law. A newly proposed eight-node element is carefully verified using various numerical experiments intended to discover possible locking phenomena. In the introduced plate elements, the usage of polynomial approximations of second order in all three directions is found to be advantageous in terms of numerical performance. A comparison of the proposed eight-node element to the introduced four-node higher-order plate elements reveals that the usage of in-plane slopes as nodal degrees of freedom has a negative effect on numerical convergence properties in thin-plate use-cases.

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