scholarly journals Periodic Properties of 1D FE Discrete Models in High Frequency Dynamics

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
A. Żak ◽  
M. Krawczuk ◽  
M. Palacz
Keyword(s):  
Finite Element ◽  
High Frequency ◽  
Strain Field ◽  
Elementary Theory ◽  
Low Frequency ◽  
Discrete Models ◽  
Stress Strain ◽  
Structural Responses ◽  
Computational Aspects ◽  
Structural Periodicity

Finite element discrete models of various engineering 1D structures may be considered as structures of certain periodic characteristics. The source of this periodicity comes from the discontinuity of stress/strain field between the elements. This behaviour remains unnoticeable, when low frequency dynamics of these structures is investigated. At high frequency regimes, however, its influence may be strong enough to dominate calculated structural responses distorting or even falsifying them completely. In this paper, certain computational aspects of structural periodicity of 1D FE discrete models are discussed by the authors. In this discussion, the authors focus their attention on an exemplary problem of 1D rod modelled according to the elementary theory.

scholarly journals THE EQUILIBRIUM FINITE ELEMENTS IN COMPUTATION OF ELASTIC STRUCTURES

1995 ◽  
Vol 1 (1) ◽  
pp. 25-47
Author(s):  
S. Kalanta
Keyword(s):  
Finite Element ◽  
Strain Field ◽  
Theoretical Background ◽  
Equilibrium Equations ◽  
Elastic Structures ◽  
Stress Strain ◽  
Flexibility Matrix ◽  
Computation Algorithms ◽  
Compatible Elements ◽  
Element Method

A problem of elastic structures stress-strain field determination is considered in this article. A theoretical background and computation algorithms of equilibrium finite element method are presented there. The different external effects are estimated, namely: load, prestressing, inicial strains and support settlements. The dual relationships (equilibrium and geometrical equations, stiffness and flexibility equations) of equilibrium element, also the expressions of stiffness and flexibility matrices are given. These relationships describe the stress-strain field of the finite element and allow to transforme the flexibility matrix to the stiffness matrix and on the contrary. There are presented direct and variational formulations of the problem. The algorithms of the forces method and displacements method are made for their solution. Easier is the algorithm of displacements method, because making equations of the forces method needs to solve the system of equilibrium equations. But the formulation and solving of the displacements equations can be changed by direct formulation of global flexibility matrix of the structure. In these cases, when the degree of static indeterminacy of the discrete model of structure is quite less than the number of freedom degrees, suth the change can be effective. The computational results illustrate the high accuracy of equilibrium elements not only with respect to forces, but also to displacements. The direct stiffness method in equilibrium elements makes it possible not only to simplify significantly implementation of the equilibrium element method, but also to include equilibrium elements in libraries of geometrically compatible elements.

Geomechanical Template for Distributed Acoustic Sensing Strain Patterns during Hydraulic Fracturing

SPE Journal ◽  
2021 ◽  
pp. 1-12
Author(s):  
Yunhui Tan ◽  
Shugang Wang ◽  
Margaretha C. M. Rijken ◽  
Kelly Hughes ◽  
Ivan Lim Chen Ning ◽  
...  
Keyword(s):  
Finite Element ◽  
Hydraulic Fracturing ◽  
Strain Rate ◽  
Hydraulic Fracture ◽  
Strain Field ◽  
Low Frequency ◽  
Fracture Propagation ◽  
Fracture Network ◽  
Hydraulic Fractures ◽  
Distributed Acoustic Sensing

Summary Recently more distributed acoustic sensing (DAS) data have been collected during hydraulic fracturing in shale. Low-frequency DAS signals show patterns that are intuitively consistent with the understanding of the strain field around hydraulic fractures. This study uses a fracture simulator combined with a finite element solver to further understand the various patterns of the strain field caused by hydraulic fracturing. The results can serve as a “type-curve” template for the further interpretation of cross-well strain field plots. Incorporating detailed pump schedule and fracturing fluid/proppant properties, we use a hydraulic fracture simulator to generate fracture geometries, which are then passed to a finite element solver as boundary conditions for elastic-static calculation of the strain field. Because the finite element calculated strain is a tensor, it needs to be projected along the monitoring well trajectory to be comparable with the DAS strain, which is uniaxial. Moreover, the calculated strain field is transformed into a time domain using constant fracture propagation velocity. Strain rate is further derived from the simulated strain field using differentiation along the fracture propagation direction. Scenarios including a single planar hydraulic fracture, a single fracture with a discrete fracture network (DFN), and multiple planar hydraulic fractures in both vertical and horizontal directions were studied. The scenarios can be differentiated in the strain patterns on the basis of the finite element simulation results. In general, there is a tensile heart-shaped zone in front of the propagating fracture tip shown along the horizontal strain direction on both strain and strain rate plots. On the sides, there are compressional zones parallel to the fracture. The strain field projects beyond the depth where the hydraulic fracture is present. Patterns from strain rate can be used to distinguish whether the fracture is intersecting the fiber. Along the vertical direction, the transition zone depicts the upper boundary of the fracture. A complex fracture network with DFN shows a much more complex pattern compared with a single planar fracture. Multiple planar fractures show polarity reversals in horizontal fiber because of interactions between fractures. Data from the Hydraulic Fracturing Test Site 2 (HFTS2) experiment were used to validate the simulated results. The application of the study is to provide a template to better interpret hydraulic fracture characteristics using low-frequency DAS strain-monitoring data. To our understanding, there are no comprehensive templates for engineers to understand the strain signals from cross-well fiber monitoring. The results of this study will guide engineers toward better optimization of well spacing and fracturing design to minimize well interference and improve efficiency.

Numerical Simulation Analysis of H-Beam Steel Controlled Cooling

2013 ◽  
Vol 395-396 ◽  
pp. 1184-1189 ◽  
Author(s):  
Xiao Guang Yu ◽  
Xu Hao ◽  
Rui Miao
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Strain Field ◽  
Simulation Analysis ◽  
Element Model ◽  
Controlled Cooling ◽  
Stress Strain ◽  
Element Analysis ◽  
Beam Cooling ◽  
H Beam

The finite element analysis software soft ANSYS is used for researching H-beam hot rolling finite element model, temperature field and stress strain field. Then find the changes law in different water cooling conditions of the temperature field temperature distribution and the stress strain field. Find the heat coefficient of H-beam by using the optimization analysis to reduce the differences of the temperature and the stress strain value, and also reduce the deformation in H-beam cooling process. The controlled cooling parameters of H-beam under optimal conditions are determined by the simulation experiment and comparative analysis. While exploring the changes of H-beam microstructure, stress and hardness can provide the reference for the making and designing of reasonable controlled cooling technology.

scholarly journals Nonlinear Behaviour of Concrete Buttress Dams under High-Frequency Excitations Taking into Account Topographical Amplifications

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Roghayeh Abbasiverki ◽  
Richard Malm ◽  
Anders Ansell ◽  
Erik Nordström
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
High Frequency ◽  
Free Field ◽  
Low Frequency ◽  
Nonlinear Behaviour ◽  
One Dimensional ◽  
Field Modelling ◽  
Stream Direction ◽  
Modelling Approach

Concrete buttress dams could potentially be susceptible to high-frequency vibrations, especially in the cross-stream direction, due to their slender design. Previous studies have mainly focused on low-frequency vibrations in stream direction using a simplified foundation model with the massless method, which does not consider topographic amplifications. This paper therefore investigates the nonlinear behaviour of concrete buttress dams subjected to high-frequency excitations, considering cross-stream vibrations. For comparison, the effect of low-frequency excitations is also investigated. The influence of the irregular topography of the foundation surface on the amplification of seismic waves at the foundation surface and thus in the dam is considered by a rigorous method based on the domain-reduction method using the direct finite element method. The sensitivity of the calculated response of the dam to the free-field modelling approach is investigated by comparing the result with analyses using an analytical method based on one-dimensional wave propagation theory and a massless approach. Available deconvolution software is based on the one-dimensional shear wave propagation to transform the earthquake motion from the foundation surface to the corresponding input motion at depth. Here, a new deconvolution method for both shear and pressure wave propagation is developed based on an iterative time-domain procedure using a one-dimensional finite element column. The examples presented showed that topographic amplifications of high-frequency excitations have a significant impact on the response of this type of dam. Cross-stream vibrations reduced the safety of the dam due to the opening of the joints and the increasing stresses. The foundation modelling approach had a significant impact on the calculated response of the dam. The massless method produced unreliable results, especially for high-frequency excitations. The free-field modelling with the analytical method led to unreliable joint openings. It is therefore recommended to use an accurate approach for foundation modelling, especially in cases where nonlinearity is considered.

scholarly journals Analytic Model of Microcantilevers as Low Frequency Generator

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Sandeep Arya ◽  
Saleem Khan ◽  
Parveen Lehana
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Frequency ◽  
Low Frequency ◽  
Signal Generator ◽  
Analytic Model ◽  
Frequency Signal ◽  
Frequency Generator ◽  
Analytic Signals ◽  
Element Method

Finite element method (FEM) based simulation has been carried out, and an analytic model of microcantilevers using piezoelectric excitations is proposed. The model is based on the type of the selected material and geometry of the structure. The investigations are carried out with rectangular microcantilevers using silicon as the substrate. The high frequency analytic signals are applied to the input piezoelectric electrodes, and the resultant signal generated at the output piezoelectric electrode is recorded and analyzed. The analysis of the results showed that the proposed system is capable of generating a low frequency signal. Two microcantilevers with different dimensional aspects are used, and the results verified the application of microcantilever array as a low frequency signal generator.

scholarly journals Mathematical and laboratory modeling of resonant impact on the spike for the purpose of grain selection

2020 ◽  
Vol 210 ◽  
pp. 05017
Author(s):  
Arkady Soloviev ◽  
Andrey Matrosov ◽  
Ivan Panfilov ◽  
Besarion Meskhi ◽  
Oleg Polushkin ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Resonance Frequency ◽  
High Frequency ◽  
Low Frequency ◽  
Element Model ◽  
Laboratory Modeling ◽  
Full Scale Experiment ◽  
High Frequency Vibrations ◽  
Scale Experiment

Mathematical and computer finite element model in the ACELAN package of resonant impact on a spike was developed and a full-scale experiment was carried out. Two installations are considered, one based on a cantilever, the free end of which acts on the spike, and the second is a semi-passive round bimorph. Excitation of vibrations is carried out using an actuator based on piezoceramic elements. In the first installation, low-frequency vibrations of the stem with a spike are excited and the resonance frequency is determined at which only an spike with grain performs intense vibrations. The second installation is designed to excite high-frequency vibrations at which resonant movements of the grains themselves arise. The purpose of both installations is to separate the grain from the spike using resonance phenomena.

Simulation of the Stress-Strain State of Diesel Engine Pistons Taking into Account Inelastic Deformations

2020 ◽  
pp. 29-36
Author(s):  
L.L. Myagkov ◽  
S.M. Sivachev
Keyword(s):  
Finite Element ◽  
Diesel Engines ◽  
Strain State ◽  
Low Frequency ◽  
Uniaxial Tensile ◽  
Creep Tests ◽  
Stress Strain ◽  
Element Analysis ◽  
Stress Strain State ◽  
Creep Models

The failure of aluminum pistons of diesel engines is often associated with formation of cracks originating at the bowl rim. The appearance of cracks is a consequence of thermal fatigue of the material due to low-frequency cycles of heating and cooling of the piston during the engine start-up, operation at various speed and load conditions, and subsequent shutdown. To assess the lifetime of the bowl rim, it is necessary to simulate non-isothermal elastoplastic deformation of the alloy using material plasticity and creep models available in finite element analysis software (e.g. ANSYS). This paper presents the results of uniaxial tensile and creep tests of proportional specimens made from piston blanks of the V-type diesel engines YaMZ-658. The piston material is AlSi12CuNiMg silumin alloy. The article describes methods for determining constants in plasticity and creep models. The results of numerical simulation of the piston’s stress-strain state for the start — nominal power mode — stop cycle using the finite element method are presented. Conclusions about the presence of plastic and creep strains at the piston edge are drawn.

Finite Element Analysis of Piezoelectric Materials

2013 ◽  
Vol 860-863 ◽  
pp. 872-875
Author(s):  
Ai Guo Zhang ◽  
Tie Jun Yang ◽  
Jing Tao Du ◽  
Peng Lv ◽  
Xin Guang Li
Keyword(s):  
Finite Element ◽  
High Frequency ◽  
Piezoelectric Materials ◽  
Low Frequency ◽  
Signal Frequency ◽  
Affecting Factors ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
Voltage Signal ◽  
Simulation Results

The ANSYS finite element techniques were used for modeling and analysis of piezoelectric materials. The single piezoelectric sheet model was presented. The basic characteristic of the piezoelectric materials were analyzed and the affecting factors of characteristics were derived. The high frequency simulation results showed that the displacement responses of piezoelectric materials were very large delay in boost and buck under the high frequency voltage signal, and that was adverse to the vibration control. The low frequency voltage simulation results showed that the displacement response frequency and voltage signal frequency were exactly the same. The model thickness greatly affected its stiffness and indirectly affected its output characteristics.

scholarly journals A LOW-HIGH FREQUENCY FORMULATION FOR FAST ACOUSTIC CALCULATIONS

2012 ◽  
Vol 20 (03) ◽  
pp. 1250011 ◽  
Author(s):  
SÉBASTIEN BESSET
Keyword(s):  
Finite Element ◽  
High Frequency ◽  
Low Cost ◽  
Low Frequency ◽  
Mesh Size ◽  
Frequency Range ◽  
Medium Frequency ◽  
Element Mesh ◽  
Cost Calculations ◽  
Acoustic Cavities

Noise predictions in acoustic cavities lead to different formulations in low or high frequency ranges. In the case of fast calculations, we propose a mixed formulation based on a finite element mesh including a "high frequency energy degree of freedom" to predict high frequency phenomena. The mesh size is planned for studying low-(medium) frequency range phenomena through a classical finite element method. The same mesh is used to build energy elements to take into account the (medium)-high frequency range phenomena. The method aims at performing low-cost calculations in medium-high frequency ranges using low-frequency-based existing meshes, i.e. without re-meshing the system.

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