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.

Large-Deformation Analysis of Elastomeric Structures by Carrera Unified Formulation

2019 ◽  
Author(s):  
E. Carrera ◽  
A. Pagani ◽  
B. Wu ◽  
M. Filippi
Keyword(s):  
Large Deformation ◽  
Virtual Work ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Approximation Order ◽  
Deformation Tensor ◽  
Deformation Analysis ◽  
Element Approximation ◽  
Slightly Compressible ◽  
Carrera Unified Formulation

Abstract Based on the well-known nonlinear hyperelasticity theory and by using the Carrera Unified Formulation (CUF) as well as a total Lagrangian approach, the unified theory of slightly compressible elastomeric structures including geometrical and physical nonlinearities is developed in this work. By exploiting CUF, the principle of virtual work and a finite element approximation, nonlinear governing equations corresponding to the slightly compressible elastomeric structures are straightforwardly formulated in terms of the fundamental nuclei, which are independent of the theory approximation order. Accordingly, the explicit forms of the secant and tangent stiffness matrices of the unified 1D beam and 2D plate elements are derived by using the three-dimensional Cauchy-Green deformation tensor and the nonlinear constitutive equation for slightly incompressible hyperelastic materials. Several numerical assessments are conducted, including uniaxial tension nonlinear response of rectangular elastomeric beams. Our numerical findings demonstrate the capabilities of the CUF model to calculate the large-deformation equilibrium curves as well as the stress distributions with high accuracy.

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.

Large Deformation Analysis of Elastic Cosserat Continua by FEM

2006 ◽  
Author(s):  
Ehsan Sharbati ◽  
Reza Naghdabadi
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Degrees Of Freedom ◽  
Strain Tensor ◽  
Cosserat Continuum ◽  
Deformation Analysis ◽  
Element Formulation ◽  
Large Deformation Analysis ◽  
Cosserat Continua ◽  
Finite Element Formulations

Based on the non linear terms appearing in the strain tensor in classical continuum mechanics, two expressions for large strain in the Cosserat continuum are proposed. The generalized form of principal of virtual work together with the constitutive equations for an isotropic elastic Cosserat continuum are used to derive the finite element formulations for elastic large deformation analysis based on the Cosserat theory. The finite element formulations are then applied to a four-node quadrilateral element with three degrees of freedom at each node including two translational and one rotational degrees of freedom. The tension of a semi-infinite plate with a circular whole in the center is solved using the Cosserat finite element formulation and the results are compared with those obtained by the classical theory. Also, pure bending and shear of a cantilever beam are done and the differences of the results obtained based on the two proposed formulations of large strains are investigated.

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