scholarly journals Isogeometric Implementation of High-Order Microplane Model for the Simulation of High-Order Elasticity, Softening, and Localization

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Erol Lale ◽  
Xinwei Zhou ◽  
Gianluca Cusatis
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Control Point ◽  
Three Dimensional ◽  
Local Strain ◽  
High Order ◽  
Particle Model ◽  
Displacement Fields ◽  
Displacement Based ◽  
The Continuum

In this paper, a recently developed higher-order microplane (HOM) model for softening and localization is implemented within a isogeometric finite-element framework. The HOM model was derived directly from a three-dimensional discrete particle model, and it was shown to be associated with a high-order continuum characterized by independent rotation and displacement fields. Furthermore, the HOM model possesses two characteristic lengths: the first associated with the spacing of flaws in the material internal structure and related to the gradient character of the continuum; the second associated with the size of these flaws and related to the micropolar character of the continuum. The displacement-based finite element implementation of this type of continua requires C1 continuity both within the elements and at the element boundaries. This motivated the implementation of the concept of isogeometric analysis which ensures a higher degree of smoothness and continuity. Nonuniform rational B-splines (NURBS) based isogeometric elements are implemented in a 3D setting, with both displacement and rotational degrees-of-freedom at each control point. The performed numerical analyses demonstrate the effectiveness of the proposed HOM model implementation to ensure optimal convergence in both elastic and softening regime. Furthermore, the proposed approach allows the natural formulation of a localization limiter able to prevent strain localization and spurious mesh sensitivity known to be pathological issues for typical local strain-softening constitutive equations.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

scholarly journals Free and Forced Vibration of Laminated and Sandwich Plates by Zig-Zag Theories Differently Accounting for Transverse Shear and Normal Deformability

Aerospace ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 108 ◽  
Author(s):  
Ugo Icardi ◽  
Andrea Urraci
Keyword(s):  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Interfacial Stress ◽  
Sandwich Plates ◽  
Displacement Fields ◽  
Element Analysis ◽  
Out Of Plane ◽  
Elasticity Solutions ◽  
Displacement Based

A number of mixed and displacement-based zig-zag theories are derived from the zig-zag adaptive theory (ZZA). As a consequence of their different assumptions on displacement, strain, and stress fields, and layerwise functions, these theories account for the transverse shear and normal deformability in different ways, but their unknowns are independent of the number of layers. Some have features that are reminiscent of ones that have been published in the literature for the sake of comparison. Benchmarks with different length-to-thickness ratios, lay-ups, material properties, and simply supported or clamped edges are studied with the intended aim of contributing toward better understanding the influence of transverse anisotropy on free vibration and the response of blast-loaded, multilayered, and sandwich plates, as well as enhancing the existing database. The results show that only theories whose layerwise contributions identically satisfy interfacial stress constrains and whose displacement fields are redefined for each layer provide results that are in agreement with elasticity solutions and three-dimensional (3D) finite element analysis (FEA) (mixed solid elements with displacements and out-of-plane stresses as nodal degrees of freedom (d.o.f.)) with a low expansion order of polynomials in the in-plane and out-of-plane directions. The choice of their layerwise functions is shown to be immaterial, while theories with fixed kinematics are shown to be strongly case-sensitive and often inadequate (even for slender components).

Prediction of Blade Flutter in a Tuned Rotor

1985 ◽  
Author(s):  
Jianmin Xu ◽  
Zhaohong Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Rotating Blades ◽  
Multiple Degrees Of Freedom ◽  
Strip Theory ◽  
Blade Flutter ◽  
Good Agreement

This paper is about blade flutter in a tuned rotor. With the aid of the combination of three dimensional structural finite element method, two dimensional aerodynamical finite difference method and strip theory, the quasi-steady models in which two degrees of freedom for a single wing were considered have been extended to multiple degrees of freedom for the whole blade in a tuned rotor. The eigenvalues solved from the blade motion equation have been used to judge whether the system is stable or not. The calculating procedure has been formed and using it the first stage rotating blades of a compressor where flutter had occurred, have been predicted. The numerical flutter boundaries have good agreement with the experimental ones.

Algorithms for the calculation of X-ray diffraction patterns from finite element data

2010 ◽  
Vol 43 (6) ◽  
pp. 1287-1299 ◽  
Author(s):  
E. Wintersberger ◽  
D. Kriegner ◽  
N. Hrauda ◽  
J. Stangl ◽  
G. Bauer
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Point Of View ◽  
X Ray Diffraction ◽  
Displacement Fields ◽  
X Ray ◽  
Si Substrates ◽  
Diffraction Patterns ◽  
Simulation Point ◽  
Ccd Detectors

A set of algorithms is presented for the calculation of X-ray diffraction patterns from strained nanostructures. Their development was triggered by novel developments in the recording of scattered intensity distributions as well as in simulation practice. The increasing use of two-dimensional CCD detectors in X-ray diffraction experiments, with which three-dimensional reciprocal-space maps can be recorded in a reasonably short time, requires efficient simulation programs to compute one-, two- and three-dimensional intensity distributions. From the simulation point of view, the finite element method (FEM) has become the standard tool for calculation of the strain and displacement fields in nanostructures. Therefore, X-ray diffraction simulation programs must be able to handle FEM data properly. The algorithms presented here make use of the deformation fields calculated on a mesh, which are directly imported into the calculation of diffraction patterns. To demonstrate the application of the developed algorithms, they were applied to several examples such as diffraction data from a dislocated quantum dot, from a periodic array of dislocations in a PbSe epilayer grown on a PbTe pseudosubstrate, and from ripple structures at the surface of SiGe layers deposited on miscut Si substrates.

A Parallel Computational Model for Three-Dimensional, Thermo-Mechanical Stokes Flow Simulations of Glaciers and Ice Sheets

2014 ◽  
Vol 16 (4) ◽  
pp. 1056-1080 ◽  
Author(s):  
Wei Leng ◽  
Lili Ju ◽  
Max Gunzburger ◽  
Stephen Price
Keyword(s):  
Finite Element ◽  
Computational Model ◽  
Stokes Flow ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Iterative Solution ◽  
Element Model ◽  
High Order

AbstractThis paper focuses on the development of an efficient, three-dimensional, thermo-mechanical, nonlinear-Stokes flow computational model for ice sheet simulation. The model is based on the parallel finite element model developed in [14] which features high-order accurate finite element discretizations on variable resolution grids. Here, we add an improved iterative solution method for treating the nonlinearity of the Stokes problem, a new high-order accurate finite element solver for the temperature equation, and a new conservative finite volume solver for handling mass conservation. The result is an accurate and efficient numerical model for thermo-mechanical glacier and ice-sheet simulations. We demonstrate the improved efficiency of the Stokes solver using the ISMIP-HOM Benchmark experiments and a realistic test case for the Greenland ice-sheet. We also apply our model to the EISMINT-II benchmark experiments and demonstrate stable thermo-mechanical ice sheet evolution on both structured and unstructured meshes. Notably, we find no evidence for the “cold spoke” instabilities observed for these same experiments when using finite difference, shallow-ice approximation models on structured grids.

Dynamic Finite Element Analysis of a Highly Parallel Robotic Surface

2011 ◽  
Author(s):  
Chris Salisbury
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Element Analysis ◽  
Revolute Joints ◽  
Stiffness Matrices ◽  
Joint Forces ◽  
Ricatti Equation ◽  
Optimal Dynamic

A novel three-dimensional robotic surface is devised using triangular modules connected by revolute joints that mimic the constraints of a spherical joint at each triangle intersection. The finite element method (FEM) is applied to the dynamic loading of this device using three dimensional (6 degrees of freedom) beam elements to not only calculate the cartesian displacement and force, but also the angular displacement and torque at each joint. In this way, the traditional methods of finding joint forces and torques are completely bypassed. An effiecient algorithm is developed to linearly combine local mass and stiffness matrices into a full structural stiffness matrix for the easy application of loads. An analysis of optimal dynamic joint forces is carried out in Simulink® with the use of an algebraic Ricatti equation.

A viscoelastic Timoshenko shaft finite element for dynamic analysis of rotors

2016 ◽  
Vol 24 (11) ◽  
pp. 2180-2200 ◽  
Author(s):  
Smitadhi Ganguly ◽  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Elastic Strain ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Viscoelastic Behavior ◽  
Beam Shape ◽  
Unit Step ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
The Time Domain

A new shaft element is proposed for viscoelastic rotors in a spinning frame considering the shear deformation in addition to bending deformation. The Maxwell–Wiechert model is considered here to replicate linear viscoelastic behavior. This model considers additional internal damping displacement variables between elastic and viscous elements and the stress depends not only on the elastic strain and elastic strain rate, but also on additional strains and their rates corresponding to the damping variables. The present work assumes that these additional strains can be derived from continuous fictitious displacement variables, which in turn are interpolated from their nodal values using the Timoshenko beam shape functions. Therefore, in addition to the standard degrees of freedom for a three-dimensional shaft, extra degrees of freedom are defined at the nodes. The finite element matrices are assembled in state space. The time domain equations are then used for stability analysis and computation of response to a unit step load and an unbalance.

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