scholarly journals Steady-State Harmonic Vibrations of Viscoelastic Timoshenko Beams with Fractional Derivative Damping Models

2021 ◽  
Vol 2 (4) ◽  
pp. 797-819
Author(s):  
Michael Klanner ◽  
Marcel S. Prem ◽  
Katrin Ellermann
Keyword(s):  
Broad Class ◽  
Time Derivative ◽  
Measurement Data ◽  
Solution Process ◽  
Viscoelastic Behavior ◽  
Beam Theory ◽  
Material Model ◽  
Computational Method ◽  
Advanced Materials ◽  
Fractional Time Derivative

Due to growing demands on newly developed products concerning their weight, sound emission, etc., advanced materials are introduced in the product designs. The modeling of these materials is an important task, and a very promising approach to capture the viscoelastic behavior of a broad class of materials are fractional time derivative operators, since only a small number of parameters is required to fit measurement data. The fractional differential operator in the constitutive equations introduces additional challenges in the solution process of structural models, e.g., beams or plates. Therefore, a highly efficient computational method called Numerical Assembly Technique is proposed in this paper to tackle general beam vibration problems governed by the Timoshenko beam theory and the fractional Zener material model. A general framework is presented, which allows for the modeling of multi-span beams with general linear supports, rigid attachments, and arbitrarily distributed force and moment loading. The efficiency and accuracy of the method is shown in comparison to the Finite Element Method. Additionally, a validation with experimental results for beam systems made of steel and polyvinyl chloride is presented, to illustrate the advantages of the proposed method and the material model.

Fractional abstract Cauchy problem on complex interpolation scales

2020 ◽  
Vol 23 (4) ◽  
pp. 1125-1140
Author(s):  
Andriy Lopushansky ◽  
Oleh Lopushansky ◽  
Anna Szpila
Keyword(s):  
Cauchy Problem ◽  
Time Derivative ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Sectorial Operator ◽  
Complex Interpolation ◽  
Bounded Domains ◽  
Initial Boundary Value Problems ◽  
Fractional Time Derivative ◽  
Initial Boundary Value

AbstractAn fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

scholarly journals New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed S. Al-luhaibi
Keyword(s):  
Iterative Method ◽  
Analytical Solutions ◽  
Gas Dynamics ◽  
Time Derivative ◽  
Explicit Solutions ◽  
Fractional Partial Differential Equations ◽  
Approximate Analytical Solutions ◽  
Fractional Time Derivative ◽  
Burger's Equations ◽  
New Iterative Method

This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

Efficient Finite Element for Evaluation of Strain Concentrations in Concrete Coated Pipelines

2008 ◽  
Author(s):  
Svein Sævik ◽  
Martin Storheim ◽  
Erik Levold
Keyword(s):  
Finite Element ◽  
Numerical Study ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Material Model ◽  
Body Motion ◽  
Theoretical Formulation ◽  
Concrete Material ◽  
Non Linear ◽  
Full Scale Tests

MARINTEK has developed software for detailed analysis of pipelines during installation and operation. As part of the software development a new coating finite element was developed in cooperation with StatoilHydro enabling efficient analysis of field joint strain concentrations of long concrete coated pipeline sections. The element was formulated based on sandwich beam theory and application of the Principle of Potential Energy. Large deformations and non-linear geometry effects were handled by a Co-rotated “ghost” reference description where elimination of rigid body motion was taken care of by referring to relative displacements in the strain energy term. The non-linearity related to shear interaction and concrete material behaviour was handled by applying non-linear springs and a purpose made concrete material model. The paper describes the theoretical formulation and numerical studies carried out to verify the model. The numerical study included comparison between model and full-scale tests as well as between model and other commercial software. At last a 3000 m long pipeline was analysed to demonstrate the strain concentration behaviour of a concrete coated pipeline exposed to high temperature snaking on the seabed.

scholarly journals Role of smooth muscle activation in the static and dynamic mechanical characterization of human aortas

2022 ◽  
Vol 119 (3) ◽  
pp. e2117232119
Author(s):  
Giulio Franchini ◽  
Ivan D. Breslavsky ◽  
Francesco Giovanniello ◽  
Ali Kassab ◽  
Gerhard A. Holzapfel ◽  
...  
Keyword(s):  
Experimental Data ◽  
Smooth Muscle ◽  
Muscle Activation ◽  
Mechanical Response ◽  
Mechanical Characterization ◽  
Viscoelastic Behavior ◽  
Material Model ◽  
Suitable Material ◽  
Dynamic Mechanical

Experimental data and a suitable material model for human aortas with smooth muscle activation are not available in the literature despite the need for developing advanced grafts; the present study closes this gap. Mechanical characterization of human descending thoracic aortas was performed with and without vascular smooth muscle (VSM) activation. Specimens were taken from 13 heart-beating donors. The aortic segments were cooled in Belzer UW solution during transport and tested within a few hours after explantation. VSM activation was achieved through the use of potassium depolarization and noradrenaline as vasoactive agents. In addition to isometric activation experiments, the quasistatic passive and active stress–strain curves were obtained for circumferential and longitudinal strips of the aortic material. This characterization made it possible to create an original mechanical model of the active aortic material that accurately fits the experimental data. The dynamic mechanical characterization was executed using cyclic strain at different frequencies of physiological interest. An initial prestretch, which corresponded to the physiological conditions, was applied before cyclic loading. Dynamic tests made it possible to identify the differences in the viscoelastic behavior of the passive and active tissue. This work illustrates the importance of VSM activation for the static and dynamic mechanical response of human aortas. Most importantly, this study provides material data and a material model for the development of a future generation of active aortic grafts that mimic natural behavior and help regulate blood pressure.

A Molecular Structure-Informed Viscoelastic Constitutive Model for Natural Rubber Materials

2021 ◽  
Author(s):  
Jiwon Jung ◽  
Chanwook Park ◽  
myungshin RYU ◽  
Gunjin Yun
Keyword(s):  
Molecular Structure ◽  
Constitutive Equation ◽  
Molecular System ◽  
Loss Modulus ◽  
Low Frequency ◽  
Viscoelastic Behavior ◽  
Material Model ◽  
Coarse Grained ◽  
Diffusivity Coefficient ◽  
Element Analysis

Abstract This paper presents a molecular structure-informed viscoelastic constitutive equation that adopts the Doi-Edward’s tube model with coarse-grained molecular dynamics (MD) simulation and primitive path analysis. Since this model contains polymer physics-related parameters directly obtained from molecular simulations, it can reflect molecular information in predictions of the viscoelastic behavior of elastomers, unlike other empirical models. The proposed incremental formulations and constitutive stiffness matrix were implemented into implicit finite element analysis (FEA) codes as a user-supplied material model and viscoelastic properties (storage, loss modulus, and tan⁡δ) were calculated from the constitutive equation. While obtaining polymer dynamics parameter of the molecular system, a relationship between self-diffusivity coefficient (D_c) and the polymerization degree of the polymer was confirmed. Furthermore, a series of parametric studies showed that increase of the primitive path length (L) and decrease of D_c have led to the strengthening of moduli and decrease of tan⁡δ peak. Moreover, under the same condition, the shift of tan⁡δ peak to low-frequency domain was observed, which implies a decline in free volume in the molecular system and an increase in the glass transition temperature.

scholarly journals ExpansionHunter: a sequence-graph-based tool to analyze variation in short tandem repeat regions

2019 ◽  
Vol 35 (22) ◽  
pp. 4754-4756 ◽  
Author(s):  
Egor Dolzhenko ◽  
Viraj Deshpande ◽  
Felix Schlesinger ◽  
Peter Krusche ◽  
Roman Petrovski ◽  
...  
Keyword(s):  
Tandem Repeat ◽  
Broad Class ◽  
Source Code ◽  
Computational Method ◽  
Supplementary Information ◽  
Dna Repeats ◽  
Supplementary Data ◽  
Sequence Graph ◽  
Version 2.0 ◽  
Short Tandem

Abstract Summary We describe a novel computational method for genotyping repeats using sequence graphs. This method addresses the long-standing need to accurately genotype medically important loci containing repeats adjacent to other variants or imperfect DNA repeats such as polyalanine repeats. Here we introduce a new version of our repeat genotyping software, ExpansionHunter, that uses this method to perform targeted genotyping of a broad class of such loci. Availability and implementation ExpansionHunter is implemented in C++ and is available under the Apache License Version 2.0. The source code, documentation, and Linux/macOS binaries are available at https://github.com/Illumina/ExpansionHunter/. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Design of Self-Supported 3D Printed Parts for Fused Deposition Modeling

2016 ◽  
Author(s):  
Fabian Lischke ◽  
Andres Tovar
Keyword(s):  
Numerical Model ◽  
Fused Deposition Modeling ◽  
Beam Theory ◽  
Critical Factor ◽  
Acrylonitrile Butadiene Styrene ◽  
Material Model ◽  
Analytical Models ◽  
Element Analysis ◽  
Fused Deposition ◽  
3D Printed

One of the primary challenges faced in Additive Manufacturing (AM) is reducing the overall cost and printing time. A critical factor in cost and time reduction is post-processing of 3D printed (3DP) parts, of which removing support structures is one of the most time consuming steps. Support is needed to prevent the collapse of the part or certain areas under its own weight during the 3D printing process. Currently, the design of self-supported 3DP parts follows a set of empirical guide lines. A trial and error process is needed to produce high quality parts by Fused Depositing Modeling (FDM). The usage of chamfer angle with a max 45° angle form the horizontal for FDM is a common example. Inclined surfaces with a smaller angle are prone to defects, however no theoretical basis has been fully defined, therefore a numerical model is needed. The model can predict the problematic areas at a print, reducing the experimental prints and providing a higher number of usable parts. Physical-based models have not been established due to the generally unknown properties of the material during the AM process. With simulations it is possible to simulate the part at different temperatures with a variety of other parameters that have influence on the behavior of the model. In this research, analytic calculations and physical tests are carried out to determine the material properties of the thermoplastic polymer Acrylonitrile - Butadiene - Styrene (ABS) f or FDM at the time of extrusion. This means that the ABS is going to be extruded at 200°C to 245°C and is a viscous material during part construction. Using the results from the physical and analytical models, i.e., Timoshenko’s modified beam theory for micro-structures, a numerical material model is established to simulate the filament deformation once it is deposited onto the part. Experiments were also used to find the threshold for different geometric specifications, which could then be applied to the numerical model to improve the accuracy of the simulation. The result of the finite element analysis is compared to experiments to show the correlation between the prediction of deflection in simulation and the actual deflection measured in physical experiments. A case study was conducted using an application that optimizes topology of complex geometries. After modeling and simulating the optimized part, areas of defect and errors were determined in the simulation, then verified and and measured with actual 3D prints.

Consequences of Viscoelastic Behavior in the Human Temporomandibular Joint Disc

2007 ◽  
Vol 86 (12) ◽  
pp. 1198-1202 ◽  
Author(s):  
J.H. Koolstra ◽  
T.M.G.J. van Eijden
Keyword(s):  
Temporomandibular Joint ◽  
Viscoelastic Behavior ◽  
Material Model ◽  
Von Mises Stress ◽  
Joint Movement ◽  
Temporomandibular Joint Disc ◽  
Apparent Stiffness ◽  
Linear Viscoelastic Material ◽  
Masticatory System ◽  
Von Mises

The consequences of the viscoelastic behavior of the temporomandibular joint disc were analyzed in simulated jaw open-close cycles. It was hypothesized that viscoelasticity helps protect the underlying bone, while augmenting the smoothness of articular movements. Simulations were performed with a dynamic model of the masticatory system, incorporating the joints’ cartilaginous structures as Finite Element Models. A non-linear viscoelastic material model was applied for the disc. The apparent stiffness of the disc to principal stress was largest when the jaw was closed, whereas, with the Von Mises’ stress, it appeared largest when the jaw was open. The apparent stiffnesses appeared to be dependent on both the speed of the movements and the presence of a resistance between the teeth. It was concluded that the disc becomes stiffer when load concentrations can be expected. During continued cyclic motion, it softens, which favors smoothness of joint movement at the cost of damage prevention.

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