An Eshelby Solution‐Based Finite‐Element Approach to Heterogeneous Fault‐Zone Modeling

2019 ◽  
Vol 91 (1) ◽  
pp. 465-474
Author(s):  
Chunfang Meng ◽  
Chen Gu ◽  
Bradford Hager
Keyword(s):  
Finite Element ◽  
Fault Zone ◽  
Degrees Of Freedom ◽  
Fault Slip ◽  
Fe Method ◽  
Host Matrix ◽  
Element Approach ◽  
Zone Modeling ◽  
Zone Microstructure ◽  
Static And Dynamic Loading

Abstract We present a fundamental solution‐based finite‐element (FE) method to homogenize heterogeneous elastic medium, that is, fault zone, under static, and dynamic loading. This method incorporates Eshelby’s strain perturbation into FE weak forms. The resulting numerical model implicitly considers the existence of inhomogeneity bodies within each element, without introducing additional degrees of freedom. The new method is implemented within an open‐source FE package that is applicable to alternating seismic and aseismic cycles. To demonstrate this method, we modify a dynamic fault‐slip problem, hosted at Southern California Earthquake Center (SCEC), by introducing a fault zone that contains different microstructures than the host matrix. The preliminary results suggest that the fault‐zone microstructure orientation has effects on fault slip, seismic arrivals and waveform frequency contents.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

scholarly journals Process Development for Integrated and Distributed Rotorcraft Design

Aerospace ◽  
2019 ◽  
Vol 6 (2) ◽  
pp. 23
Author(s):  
Peter Weiand ◽  
Michel Buchwald ◽  
Dominik Schwinn
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Process Development ◽  
Design Environment ◽  
Aerospace Medicine ◽  
System Architectures ◽  
Joint Project ◽  
Element Approach ◽  
German Aerospace ◽  
Simulation And Evaluation

The German Aerospace Center is currently developing a new design environment for rotorcraft, which combines sizing, simulation and evaluation tasks into one toolbox. The complete environment applies distributed computation on the servers of the various institutes involved. A uniform data model with a collaboration and interface software, developed by DLR and open source, are used for exchange and networking. The tools used apply blade element methods in connection with full six degrees of freedom trim, panel methods for aerodynamic loads, different empirical models for sizing, engine properties and component mass estimation and finite element methods for structural design. A special feature is the integration of a higher fidelity overall simulation tool directly into the sizing loop. The paper describes the use of the several tools for the phases of conceptual and preliminary design. A design study is presented demonstrating the sensitivity of the process for a variation of the input parameters exhibiting a broad range for trade-off studies. The possibility to continue for analyzing and sizing of the structural properties is also demonstrated by applying a finite element approach for specific load cases. These features highlight the core of the new design environment and enable the development of goal-oriented design processes for research especially of new and unconventional rotorcraft configurations. The work presented in this paper was conducted throughout the DLR internal project, namely the Technologies for Rotorcraft in Integrated and Advanced Design (TRIAD). TRIAD is a joint project of the institutes of Flight Systems, the institute of Aerodynamics and Flow Technology, the institute of Structures and Design, the System Architectures in Aeronautics and Institute of Aerospace Medicine and receives basic founding.

A Reduced Full-System Finite Element Approach to the Solution of EHL Problems: Line Contacts

2010 ◽  
Author(s):  
W. Habchi ◽  
J. Issa
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Degrees Of Freedom ◽  
Contact Problems ◽  
Full System ◽  
Acceptable Solution ◽  
Line Contacts ◽  
Order Of Magnitude ◽  
Element Approach ◽  
Basis Method

This paper presents a reduced full-system finite element solution of isothermal elastohydrodynamic (EHD) line contact problems. The proposed model is based on a full-system finite element resolution of the EHL equations: Reynolds, linear elasticity and load balance. A reduced model is proposed for the linear elasticity problem. For this, three different techniques are tested: the classical “Modal reduction” and “Ritz-vector” methods and a novel “EHL-basis” method. The reduction order in the first two appears to be insufficient and a large number of degrees of freedom is required in order to attain an acceptable solution. On the other hand, the “EHL-basis” method shows up to be much more efficient, requiring only a few degrees of freedom to compose the elastic deformation of the solid components. In addition, a comparison with the full model shows an order of magnitude cpu time gain with errors of the order of only 1‰ for the central and minimum film thicknesses.

Output-Only Modal Analysis of an Internal Unreachable Module Embedded in a Space Electronic Equipment

2012 ◽  
Author(s):  
Lassaad Ben Fekih ◽  
Georges Kouroussis ◽  
David Wattiaux ◽  
Olivier Verlinden ◽  
Christophe De Fruytier
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Degrees Of Freedom ◽  
Transverse Direction ◽  
Mode Shapes ◽  
Fe Model ◽  
Fe Method ◽  
Numeric Model ◽  
Stiffness Matrices ◽  
Output Only

An approach is proposed to identify the modal properties of a subsystem made up of an arbitrary chosen inner module of embedded space equipment. An experimental modal analysis was carried out along the equipment transverse direction with references taken onto its outer housing. In parallel, a numerical model using the finite element (FE) method was developed to correlate with the measured results. A static Guyan reduction has led to a set of master degrees of freedom in which the experimental mode shapes were expanded. An updating technique consisting in minimizing the dynamic residual induced by the FE model and the measurements has been investigated. A last verification has consisted in solving the numeric model composed of the new mass and stiffness matrices obtained by means of a minimization of the error in the constitutive equation method.

A Parametric Study on the Strain Concentration in Field Joint of Concrete Coated Pipelines Using Finite Element Method

2009 ◽  
Author(s):  
Nikzad Nourpanah ◽  
Farid Taheri
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parametric Study ◽  
Concentration Factor ◽  
Geometrical Parameters ◽  
Fe Method ◽  
Strain Concentration ◽  
Finite Element Approach ◽  
Geometrical Properties ◽  
Element Approach

This paper aims at investigating the strain concentration in the field joints of concrete coated pipelines. A parametric study, using the finite element (FE) method, is conducted to investigate the effect of different geometric and material related parameters on the strain concentration. The selected parameters are believed to be the most influencing ones, and their variations selected as such, so to reflect practical situations. The finite element approach used in this study was discussed and validated by the authors in their earlier work. In this study, twenty three FE models are analyzed and their results are processed and presented in terms of variation of Strain Concentration Factor (SCF) versus the considered parameters, thus enabling us to examine the trend of variation of SCF with respect to each parameter. The observed trends and their underlying mechanics are described. Furthermore, a non-dimensional “geometric parameter” is introduced, which lumps the geometrical parameters investigated into a single parameter, such that it could adequately describe the variations of SCF. It is observed that a threshold exists for this parameter, beyond which the SCF can be deemed constant for design purposes, and below which the SCF would become very sensitive to the geometrical properties.

Finite Element Modelling of Bi-Material Interface for Crack Growth Evaluation: Technical Note

2018 ◽  
Vol 9 (5) ◽  
Author(s):  
M. Logesh ◽  
S. Palani ◽  
S. Shanmugan ◽  
M. Selvam ◽  
K.A. Harish
Keyword(s):  
Finite Element ◽  
Crack Growth ◽  
Degrees Of Freedom ◽  
Technical Note ◽  
Fe Model ◽  
J Integral ◽  
Fe Method ◽  
Material Interface ◽  
Determine Stress Intensity Factor ◽  
Fiber Metal

Finite element (FE) method is commonly used to study cracks in structures. In this paper, J-integral method is applied over FE model of a cracked body to determine stress intensity factor (SIF) in the domain of linear elastic fracture mechanics (LEFM). This paper formulates the J-integral methodology for 2D FE model using a coarse mesh with less degrees of freedom. Two cases , a finite plate with edge cracks and a normal crack growth in fiber metal laminated plate, are demonstrated. Numerical implementation and mesh refinement issues to maintain path independent J-integral values are explored.

Finite element analysis of micromorphic and micropolar continua based on two-dimensional elasticity

2018 ◽  
Vol 24 (6) ◽  
pp. 1893-1907 ◽  
Author(s):  
Majid Bazdid-Vahdati ◽  
Mohammad Faraji Oskouie ◽  
Reza Ansari ◽  
Hessam Rouhi
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Test Problems ◽  
Element Formulation ◽  
Two Dimensional ◽  
Element Analysis ◽  
Micropolar Continua ◽  
Element Approach ◽  
Micro Deformation ◽  
2D Elasticity

In this paper, within the framework of two-dimensional (2D) elasticity, a novel finite element formulation is proposed based on the micropolar theory (MPT) and the micromorphic theory (MMT). First, general formulations are developed for the micromorphic and micropolar continua in the context of 2D elasticity. Then, they are presented in a matrix form which is useful from the computational viewpoint. In the next step, using the matricized MPT and MMT formulations, a linear finite element approach including the effects of micro-deformation and micro-rotation degrees of freedom (DOFs) of material particles is developed, and a quadratic size-dependent element is proposed accordingly. Two test problems are solved to reveal the efficiency of the developed formulation. The influence of the length scale parameter on the bending of micromorphic and micropolar plates is illustrated in the given examples. Furthermore, comparisons are made between the results obtained from classical elasticity theory and those calculated based upon MPT and MMT.

Sparse tensor product finite element method for nonlinear multiscale variational inequalities of monotone type

2019 ◽  
Vol 40 (3) ◽  
pp. 1875-1907
Author(s):  
Wee Chin Tan ◽  
Viet Ha Hoang
Keyword(s):  
Finite Element ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Tensor Product ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Optimal Number ◽  
Fe Method ◽  
Logarithmic Factor ◽  
Monotone Type

Abstract We study an essentially optimal finite element (FE) method for locally periodic nonlinear multiscale variational inequalities of monotone type in a domain $D\subset{\mathbb{R}}^d$ that depend on a macroscopic and $n$ microscopic scales. The scales are separable. Using multiscale convergence we deduce a multiscale homogenized variational inequality in a tensorized domain in the high-dimensional space ${\mathbb R}^{(n+1)d}$. Given sufficient regularity on the solution the sparse tensor product FE method is developed for this problem, which attains an essentially equal (i.e., it differs by only a logarithmic factor) level of accuracy to that of the full tensor product FE method, but requires an essentially optimal number of degrees of freedom which is equal to that for solving a problem in ${{\mathbb{R}}}^d$ apart from a logarithmic factor. For two-scale problems we deduce a new homogenization error for the nonlinear monotone variational inequality. A numerical corrector is then constructed with an explicit error in terms of the homogenization and the FE errors. For general multiscale problems we deduce a numerical corrector from the FE solution of the multiscale homogenized problem, but without an explicit error as such a homogenization error is not available.

Multiple Low Velocity Impact on Twisted Composite Stiffened Blade: A Finite Element Approach

2017 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Sasank Shekhar Hota ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Shell Element ◽  
Low Velocity Impact ◽  
Stiffened Panel ◽  
Low Velocity ◽  
Finite Element Approach ◽  
Element Approach ◽  
Loading And Unloading ◽  
The Impact

This paper presents the numerical modeling of a twisted stiffened cylindrical shell employing finite element approach to investigate the transient response due to impact of multiple masses, wherein the shell and the stiffener are modeled as 8 noded isoparametric shell element with five degrees of freedom per node and 3 noded isoparametric curved beam element having four degrees of freedom per node, respectively. The stiffener element is considered as a discrete beam element and its nodal degrees of freedom are transferred to the corresponding degrees of freedom of the shell element considering curvature and eccentricity. The impact force is predicted by employing modified Hertzian contact law relating the contact force to local indentation. As indentation takes place the impactor induces damage and permanent deformation in the contact zone of stiffened panel, as a result the loading and unloading curves are different. Different mathematical equations are considered for both loading and unloading cases in the stiffened panel during low-velocity impact. The accuracy and effectiveness of the finite element approach is verified by comparing the results with the corresponding solutions of analytical as well as standard computational methods available in the open literature. The optimum design of a structure can only be obtained by understanding the impact behavior and the roles of various parameters affecting the response. Hence, parametric study has been carried out to predict the time histories of contact force, displacement of the impact point and in-plane stresses during low-velocity concurrent/delayed impact at multiple locations of the stationary and rotating stiffened shell.

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