scholarly journals Enhancing the electrical and thermal conductivities of polymer composites via curvilinear fibers: An analytical study

2019 ◽  
Vol 24 (10) ◽  
pp. 3231-3253 ◽  
Author(s):  
Marco Salviato ◽  
Sean E Phenisee
Keyword(s):  
Closed Form ◽  
Electric Conductivity ◽  
Electrostatic Potential ◽  
Mechanical Performance ◽  
Transverse Isotropy ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Closed Form Expression ◽  
Element Analysis

The new generation of manufacturing technologies such as additive manufacturing and automated fiber placement has enabled the development of material systems with desired functional and mechanical properties via particular designs of inhomogeneities and their mesostructural arrangement. Among these systems, particularly interesting are materials exhibiting curvilinear transverse isotropy (CTI), in which the inhomogeneities take the form of continuous fibers following curvilinear paths designed to, for example, optimize the electric and thermal conductivity, and the mechanical performance of the system. In this context, the present work proposes a general framework for the exact, closed-form solution of electrostatic problems in materials featuring CTI. First, the general equations for the fiber paths that optimize the electric conductivity are derived, leveraging a proper conformal coordinate system. Then, the continuity equation for the curvilinear transversely isotropic system is derived in terms of electrostatic potential. A general exact, closed-form expression for the electrostatic potential and electric field is derived and validated by finite element analysis. Finally, potential avenues for the development of materials with superior electric conductivity and damage sensing capabilities are discussed.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric Gaussian Random Walks

2019 ◽  
Keyword(s):  
Closed Form ◽  
Recursive Algorithm ◽  
Closed Form Solution ◽  
Form Solution ◽  
Closed Form Expression ◽  
Problem Solution ◽  
Underlying Asset ◽  
Quadratic Hedging ◽  
Hedging Problem ◽  
The Impact

This study obtains a closed-form solution for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. This extends the work of Rémillard and Rubenthaler (2013), who obtained closed-form formulas for some components of the hedging problem solution. Coefficients embedded in the closed-form expression can be computed either directly or through a recursive algorithm. The author also presents a brief sensitivity analysis to determine the impact of the underlying asset drift and the hedging portfolio rebalancing frequency on the optimal hedging capital and the initial hedge ratio.

EXACT PRICING WITH STOCHASTIC VOLATILITY AND JUMPS

2010 ◽  
Vol 13 (06) ◽  
pp. 901-929 ◽  
Author(s):  
FERNANDA D'IPPOLITI ◽  
ENRICO MORETTO ◽  
SARA PASQUALI ◽  
BARBARA TRIVELLATO
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Exact Algorithm ◽  
Form Solution ◽  
Closed Form Expression ◽  
Barrier Options ◽  
Form Expression ◽  
Variance Swaps ◽  
Jump Diffusion Model

A stochastic volatility jump-diffusion model for pricing derivatives with jumps in both spot return and volatility underlying dynamics is presented. This model admits, in the spirit of Heston, a closed-form solution for European-style options. The structure of the model is also suitable to explicitly obtain the fair delivery price for variance swaps. To evaluate derivatives whose value does not admit a closed-form expression, a methodology based on an "exact algorithm", in the sense that no discretization of equations is required, is developed and applied to barrier options. Goodness of pricing algorithm is tested using DJ Euro Stoxx 50 market data for European options. Finally, the algorithm is applied to compute prices and Greeks for barrier options and to determine the fair delivery prices for variance swaps.

A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Elastic Field ◽  
Form Solution ◽  
Eshelby Tensor ◽  
Cylindrical Inclusion ◽  
Closed Form Expression ◽  
Equivalent Inclusion Method ◽  
Explicit Analytical Solution ◽  
Present Solution

From the analytical formulation developed by Ju and Sun [1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574], it is seen that the exterior point Eshelby tensor for an ellipsoid inclusion possesses a minor symmetry. The solution to an elliptic cylindrical inclusion may be obtained as a special case of Ju and Sun’s solution. It is noted that the closed-form expression for the exterior-point Eshelby tensor by Kim and Lee [2010, “Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion,” ASME Trans. J. Appl. Mech., 77, p. 024503] violates the minor symmetry. Due to the importance of the solution in micromechanics-based analysis and plane-elasticity-related problems, in this work, the explicit analytical solution is rederived. Furthermore, the exterior-point Eshelby tensor is used to derive the explicit closed-form solution for the elastic field outside the inclusion, as well as to quantify the elastic field discontinuity across the interface. A benchmark problem is used to demonstrate a valuable application of the present solution in implementing the equivalent inclusion method.

Thermal Induced Stresses in Bridge-Wire Initiator Glass-to-Metal Seals

2006 ◽  
Vol 129 (3) ◽  
pp. 300-306 ◽  
Author(s):  
Luke M. Thompson ◽  
Michael R. Maughan ◽  
Karl K. Rink ◽  
Donald M. Blackketter ◽  
Robert R. Stephens
Keyword(s):  
Closed Form ◽  
Plane Stress ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Manufacturing Processes ◽  
Material Degradation ◽  
Element Analysis ◽  
Parametric Plane ◽  
Lumped Models

Cracks have been observed in the insulating glass of bridge-wire initiators that may allow moisture to penetrate the assembly, potentially leading to the corrosion and degradation of the bridge wire and the pyrotechnic material. Degradation of the pyrotechnic or the bridge wire may result in initiator failure or diminished performance. The goal of this research is to determine if the manufacturing processes could produce thermal stresses great enough to crack the glass. A parametric plane stress closed-form solution was used to determine the effects of changing material properties and dimensions of the initiator, and to determine potential stresses within the initiator from two different manufacturing scenarios. To verify and expand the plane stress closed-form solution, a two-dimensional axisymmetric finite element analysis was performed. To reproduce the two manufacturing scenarios, lumped models and models that included the effects of cooling the initiator were used. Both models showed that if the manufacturing process involves pouring molten glass into the initiator, the potential for cracking exists. Furthermore, if the surface of the initiator cools faster than the center, cracking is more likely.

scholarly journals Joint Resource Allocation for SWIPT-Based Two-Way Relay Networks

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6024
Author(s):  
Chunling Peng ◽  
Guozhong Wang ◽  
Fangwei Li ◽  
Huaping Liu
Keyword(s):  
Resource Allocation ◽  
Outage Probability ◽  
Closed Form ◽  
Time Allocation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Closed Form Expression ◽  
Power Splitting ◽  
Decode And Forward ◽  
Joint Resource Allocation

This paper considers simultaneous wireless information and power transfer (SWIPT) in a decode-and-forward two-way relay (DF-TWR) network, where a power splitting protocol is employed at the relay for energy harvesting. The goal is to jointly optimize power allocation (PA) at the source nodes, power splitting (PS) at the relay node, and time allocation (TA) of each duration to minimize the system outage probability. In particular, we propose a static joint resource allocation (JRA) scheme and a dynamic JRA scheme with statistical channel properties and instantaneous channel characteristics, respectively. With the derived closed-form expression of the outage probability, a successive alternating optimization algorithm is proposed to tackle the static JRA problem. For the dynamic JRA scheme, a suboptimal closed-form solution is derived based on a multistep optimization and relaxation method. We present a comprehensive set of simulation results to evaluate the proposed schemes and compare their performances with those of existing resource allocation schemes.

Material Property Identification of Artificial Degenerated Intervertebral Disc Models — Comparison of Inverse Poroelastic Finite Element Analysis with Biphasic Closed Form Solution

2013 ◽  
Vol 29 (4) ◽  
pp. 589-597 ◽  
Author(s):  
M. Nikkhoo ◽  
Y.-C. Hsu ◽  
M. Haghpanahi ◽  
M. Parnianpour ◽  
J.-L. Wang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Intervertebral Disc ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Hydraulic Permeability ◽  
Element Analysis ◽  
Property Identification

ABSTRACTDisc rheological parameters regulate the mechanical and biological function of intervertebral disc. The knowledge of effects of degeneration on disc rheology can be beneficial for the design of new disc implants or therapy. We developed two material property identification protocols, i.e., inverse poroelas-tic finite element analysis, and biphasic closed form solution. These protocols were used to find the material properties of intact, moderate and severe degenerated porcine discs. Comparing these two computational protocols for intact and artificial degenerated discs showed they are valid in defining bi-phasic/poroelastic properties. We found that enzymatic agent disrupts the functional interactions of proteoglycans which decreased hydraulic permeability and aggregate modulus but increased the Poisson's ratio. The fatigue loading, which damages disc structure, and squeezes and occludes the matrix pores, further decreased the hydraulic permeability and the Poisson's ratio but increased the elastic modulus. The FE simulations showed the stress experienced during the creep test increases with severe degeneration but steady-state fluid loss decreases for the both moderate and severe degenerated discs. Discriminant analysis declared that the probability of correct classification using the FE analysis is higher than the results of the closed form solution. The specimen-specific models extracted from FE analysis can be additionally used for complimentary investigations on disc biomechanics.

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