scholarly journals Fracture mechanics approach to design analysis of notches, steps, and internal cut-outs in planar components

2007 ◽  
Vol 42 (6) ◽  
pp. 433-446 ◽  
Author(s):  
T. G F Gray ◽  
J Wood
Keyword(s):  
Stress Field ◽  
Closed Form ◽  
Field Intensity ◽  
Free Boundaries ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
New Information ◽  
Intensity Information ◽  
Sharp Crack ◽  
Stress Concentration Factors

A new approach to the assessment and optimization of geometric stress-concentrating features is proposed on the basis of the correspondence between sharp crack or corner stressfield intensity factors and conventional elastic stress concentration factors (SCFs) for radiused transitions. This approach complements the application of finite element analysis (FEA) and the use of standard SCF data from the literature. The method makes it possible to develop closed-form solutions for SCFs in cases where corresponding solutions for the sharp crack geometries exist. This is helpful in the context of design optimization. The analytical basis of the correspondence is shown, together with the limits on applicability where stress-free boundaries near the stress concentrating feature are present or adjacent features interact. Examples are given which compare parametric results derived from FEA with closed-form solutions based on the proposed method. New information is given on the stress state at a 90° corner or width step, where the magnitude of the stress field intensity is related to that of the corresponding crack geometry. This correspondence enables the user to extend further the application of crack-tip stress-field intensity information to square-cornered steps, external U-grooves, and internal cut-outs.

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.

An Algorithm for Reducing the Size of Finite Element Closed-Form Source Code Files

2009 ◽  
Author(s):  
Sara McCaslin ◽  
Kent Lawrence
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Source Code ◽  
Simple Algorithm ◽  
Higher Order ◽  
Error Estimator ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Large Source

Closed-form solutions, as opposed to numerically integrated solutions, can now be obtained for many problems in engineering. In the area of finite element analysis, researchers have been able to demonstrate the efficiency of closed-form solutions when compared to numerical integration for elements such as straight-sided triangular [1] and tetrahedral elements [2, 3]. With higher order elements, however, the length of the resulting expressions is excessive. When these expressions are to be implemented in finite element applications as source code files, large source code files can be generated, resulting in line length/ line continuation limit issues with the compiler. This paper discusses a simple algorithm for the reduction of large source code files in which duplicate terms are replaced through the use of an adaptive dictionary. The importance of this algorithm lies in its ability to produce manageable source code files that can be used to improve efficiency in the element generation step of higher order finite element analysis. The algorithm is applied to Fortran files developed for the implementation of closed-form element stiffness and error estimator expressions for straight-sided tetrahedral finite elements through the fourth order. Reductions in individual source code file size by as much as 83% are demonstrated.

A New Approach to Obtaining Closed-Form Solutions for Higher Order Tetrahedral Finite Elements Using Modern Computer Algebra Systems

2011 ◽  
Author(s):  
Sara E. McCaslin ◽  
Panos S. Shiakolas ◽  
Brian H. Dennis ◽  
Kent L. Lawrence
Keyword(s):  
Parallel Processing ◽  
Closed Form ◽  
Computer Algebra ◽  
High Order ◽  
Computer Algebra Systems ◽  
Element Analysis ◽  
New Approach ◽  
Closed Form Solutions ◽  
Modern Computer ◽  
Stiffness Matrices

Closed-form solutions for straight-sided tetrahedral element stiffness matrices used in finite element analysis have been proven more efficient than numerically integrated solutions. These closed-form solutions are symbolically integrated using computer algebra systems such as Mathematica or Maple. However, even with memory and processing speed available on desktop computers today, major hindrances exist when attempting to symbolically evaluate the stiffness matrices for high order elements. This research proposes a new approach to obtaining closed-form solutions. Results are presented that demonstrate the feasibility of obtaining the stiffness matrices for high order tetrahedral elements through p-level 9 by use of parallel processing tools in Mathematica 7. Comparisons are made between serial and parallel approaches based on memory required to generate a solution. The serial approach requires more memory and can only generate closed-form solutions up to 7th order. The parallel processing approach presented requires less memory and can generate solutions up to 9th order.

scholarly journals Reconfigurable Intelligent Surface assisted Two–Way Communications: Performance Analysis and Optimization

2020 ◽  
Author(s):  
Saman Atapattu ◽  
Rongfei Fan ◽  
Prathapasinghe Dharmawansa ◽  
Gongpu Wang ◽  
JAMIE EVANS ◽  
...  
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Spectral Efficiency ◽  
Rayleigh Fading ◽  
Performance Metrics ◽  
Optimal Solution ◽  
Single Element ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Semidefinite Programming Problem

In this paper, we investigate the two-way communication between two users assisted by a re-configurable intelligent surface (RIS). The scheme that two users communicate simultaneously in the same time slot over Rayleigh fading channels is considered. The channels between the two users and RIS can either be reciprocal or non-reciprocal. For reciprocal channels, we determine the optimal phases at the RIS to maximize the signal-to-interference-plus-noise ratio (SINR). We then derive exact closed-form expressions for the outage probability and spectral efficiency for single-element RIS. By capitalizing the insights obtained from the single-element analysis, we introduce a gamma approximation to model the product of Rayleigh random variables which is useful for the evaluation of the performance metrics in multiple-element RIS. Asymptotic analysis shows that the outage decreases at $\left(\log(\rho)/\rho\right)^L$ rate where $L$ is the number of elements, whereas the spectral efficiency increases at $\log(\rho)$ rate at large average SINR $\rho$. For non-reciprocal channels, the minimum user SINR is targeted to be maximized. For single-element RIS, closed-form solutions are derived whereas for multiple-element RIS the problem turns out to be non-convex. The latter is relaxed to be a semidefinite programming problem, whose optimal solution is achievable and serves as a sub-optimal solution.

scholarly journals Reconfigurable Intelligent Surface assisted Two–Way Communications: Performance Analysis and Optimization

2020 ◽  
Author(s):  
Saman Atapattu ◽  
Rongfei Fan ◽  
Prathapasinghe Dharmawansa ◽  
Gongpu Wang ◽  
JAMIE EVANS ◽  
...  
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Spectral Efficiency ◽  
Rayleigh Fading ◽  
Performance Metrics ◽  
Optimal Solution ◽  
Single Element ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Semidefinite Programming Problem

In this paper, we investigate the two-way communication between two users assisted by a re-configurable intelligent surface (RIS). The scheme that two users communicate simultaneously in the same time slot over Rayleigh fading channels is considered. The channels between the two users and RIS can either be reciprocal or non-reciprocal. For reciprocal channels, we determine the optimal phases at the RIS to maximize the signal-to-interference-plus-noise ratio (SINR). We then derive exact closed-form expressions for the outage probability and spectral efficiency for single-element RIS. By capitalizing the insights obtained from the single-element analysis, we introduce a gamma approximation to model the product of Rayleigh random variables which is useful for the evaluation of the performance metrics in multiple-element RIS. Asymptotic analysis shows that the outage decreases at $\left(\log(\rho)/\rho\right)^L$ rate where $L$ is the number of elements, whereas the spectral efficiency increases at $\log(\rho)$ rate at large average SINR $\rho$. For non-reciprocal channels, the minimum user SINR is targeted to be maximized. For single-element RIS, closed-form solutions are derived whereas for multiple-element RIS the problem turns out to be non-convex. The latter is relaxed to be a semidefinite programming problem, whose optimal solution is achievable and serves as a sub-optimal solution.

scholarly journals Thermoelastic Closed-Form Solutions of FGM Plates Subjected to Temperature Change in Axial and Thickness Directions

2020 ◽  
Author(s):  
Yen-Ling Chung
Keyword(s):  
Closed Form ◽  
Temperature Change ◽  
Axial Force ◽  
Maximum Stress ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Bottom Surface ◽  
Thermal Loads ◽  
Element Analysis ◽  
Closed Form Solutions

Abstract An analytical solution of simply supported FGM plates under thermal loads is developed based on medium-thick plate assumption. Further to assume constant Poisson’s ratio and thermal expansion coefficient, the closed-form solutions of the FGM plates with through-the-thickness Young’s modulus under temperature change in x - and z -directions are evaluated, expressed in terms of the thermal axial force and thermal bending moment. The closed-form solutions confirmed by finite element analysis give a complete insight into the thermal-mechanical behavior of FGM plates. Hence, the deflection, strain, stress, axial force, and bending moment of the FGM plate under thermal loads in axial and thickness directions are discussed. Results show that the use of FGM makes the maximum stress from the top or bottom surface move to the inner portion of the FGM plate, and significantly reduces the maximum stress of the plates. Moreover, although the FGM plate is subjected to thermal load in the thickness direction, the deflection of the FGM plate can be zero by properly choosing the steep material gradation, directly derived from the obtained closed-form solution.

scholarly journals Applicability of the interface spring model for micromechanical analyses with interfacial imperfections to predict the modified exterior Eshelby tensor and effective modulus

2019 ◽  
Vol 24 (9) ◽  
pp. 2944-2960 ◽  
Author(s):  
Sangryun Lee ◽  
Youngsoo Kim ◽  
Jinyeop Lee ◽  
Seunghwa Ryu
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Eshelby Tensor ◽  
Effective Moduli ◽  
Spring Model ◽  
Interfacial Damage ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
The Matrix ◽  
Linear Spring

Closed-form solutions for the modified exterior Eshelby tensor, strain concentration tensor, and effective moduli of particle-reinforced composites are presented when the interfacial damage is modeled as a linear-spring layer of vanishing thickness; the solutions are validated against finite element analyses. Based on the closed-form solutions, the applicability of the interface spring model is tested by calculating those quantities using finite element analysis augmented with a matrix–inhomogeneity non-overlapping condition. The results indicate that the interface spring model reasonably captures the characteristics of the stress distribution and effective moduli of composites, despite its well-known problem of unphysical overlapping between the matrix and inhomogeneity.

Determination of Pipe Whip Restraint Location to Prevent Plastic Hinge Formation in High Energy Piping Systems

2011 ◽  
Author(s):  
Sivadol Vongmongkol ◽  
Asgar Faal-Amiri ◽  
Hari M. Srivastava
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Power Plants ◽  
Plastic Hinge ◽  
Bending Moment ◽  
High Energy ◽  
Piping System ◽  
Secondary Effects ◽  
Element Analysis ◽  
Closed Form Solutions

The purpose of this study is to determine the Pipe Whip Restraint (PWR) location that would prevent the formation of a plastic hinge due to secondary effects of a postulated pipe break load in a high energy line(1). The prevention of a plastic hinge formation at the PWR location is important since its secondary effects could lead to additional interactions with safety related equipment, structure, and component that are essential to safely shutdown the nuclear power plants. The proper location of the PWR can be found by using the relationship between bending moment-carrying capacity of the pipe and the applied thrust force. Several closed-form solutions obtained from several literatures were studied and used to calculate bending moment-carrying capacities of a piping system and ultimately used to determine a plastic hinge length. The plastic hinge formation is also determined analytically by using the Finite Element Analysis (FEA) method. ANSYS LS-DYNA® [8] Explicit Finite Element code is used in modeling the pipe whip models, which includes the piping system and pipe whip restraint. Comparisons are made between the analytical (FEA) results and the results from several closed-form solutions.

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