A Method for the Calculation of Abscissas and Weight Factors Using Gaussian Integration for Integrands with a Logarithmic Singularity

1987 ◽  
Author(s):  
Stephen A. Wilkerson
Keyword(s):  
Logarithmic Singularity ◽  
Gaussian Integration ◽  
Weight Factors

Interaction between a nanocrack with surface elasticity and a screw dislocation

2016 ◽  
Vol 22 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Xu Wang ◽  
Hui Fan
Keyword(s):  
Screw Dislocation ◽  
Real Axis ◽  
Analytical Study ◽  
Logarithmic Singularity ◽  
Surface Elasticity ◽  
Spontaneous Generation ◽  
The Real ◽  
Crack Tips ◽  
Interaction Problem ◽  
The Continuum

In the present analytical study, we consider the problem of a nanocrack with surface elasticity interacting with a screw dislocation. The surface elasticity is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. By considering both distributed screw dislocations and line forces on the crack, we reduce the interaction problem to two decoupled first-order Cauchy singular integro-differential equations which can be numerically solved by the collocation method. The analysis indicates that if the dislocation is on the real axis where the crack is located, the stresses at the crack tips only exhibit the weak logarithmic singularity; if the dislocation is not on the real axis, however, the stresses exhibit both the weak logarithmic and the strong square-root singularities. Our result suggests that the surface effects of the crack will make the fracture more ductile. The criterion for the spontaneous generation of dislocations at the crack tip is proposed.

scholarly journals ChemProps: A RESTful API enabled database for composite polymer name standardization

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Bingyin Hu ◽  
Anqi Lin ◽  
L. Catherine Brinson
Keyword(s):  
Data Exchange ◽  
Ground Truth ◽  
Training Data ◽  
Test Accuracy ◽  
Polymer Science ◽  
Data Systems ◽  
Materials Informatics ◽  
Related Data ◽  
Weight Factors ◽  
Data Points

AbstractThe inconsistency of polymer indexing caused by the lack of uniformity in expression of polymer names is a major challenge for widespread use of polymer related data resources and limits broad application of materials informatics for innovation in broad classes of polymer science and polymeric based materials. The current solution of using a variety of different chemical identifiers has proven insufficient to address the challenge and is not intuitive for researchers. This work proposes a multi-algorithm-based mapping methodology entitled ChemProps that is optimized to solve the polymer indexing issue with easy-to-update design both in depth and in width. RESTful API is enabled for lightweight data exchange and easy integration across data systems. A weight factor is assigned to each algorithm to generate scores for candidate chemical names and optimized to maximize the minimum value of the score difference between the ground truth chemical name and the other candidate chemical names. Ten-fold validation is utilized on the 160 training data points to prevent overfitting issues. The obtained set of weight factors achieves a 100% test accuracy on the 54 test data points. The weight factors will evolve as ChemProps grows. With ChemProps, other polymer databases can remove duplicate entries and enable a more accurate “search by SMILES” function by using ChemProps as a common name-to-SMILES translator through API calls. ChemProps is also an excellent tool for auto-populating polymer properties thanks to its easy-to-update design.

An inhomogeneous cell-based smoothed finite element method for the nonlinear transient response of functionally graded magneto-electro-elastic structures with damping factors

2018 ◽  
Vol 30 (3) ◽  
pp. 416-437 ◽  
Author(s):  
Liming Zhou ◽  
Ming Li ◽  
Bingkun Chen ◽  
Feng Li ◽  
Xiaolin Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Element Model ◽  
Micro Electro Mechanical System ◽  
Functionally Graded ◽  
Elastic Structures ◽  
Mapping Procedure ◽  
Gaussian Integration ◽  
Smoothed Finite Element Method ◽  
Element Method

In this article, an inhomogeneous cell-based smoothed finite element method (ICS-FEM) was proposed to overcome the over-stiffness of finite element method in calculating transient responses of functionally graded magneto-electro-elastic structures. The ICS-FEM equations were derived by introducing gradient smoothing technique into the standard finite element model; a close-to-exact system stiffness was also obtained. In addition, ICS-FEM could be carried out with user-defined sub-routines in the business software now available conveniently. In ICS-FEM, the parameters at Gaussian integration point were adopted directly in the creation of shape functions; the computation process is simplified, for the mapping procedure in standard finite element method is not required; this also gives permission to utilize poor quality elements and few mesh distortions during large deformation. Combining with the improved Newmark scheme, several numerical examples were used to prove the accuracy, convergence, and efficiency of ICS-FEM. Results showed that ICS-FEM could provide solutions with higher accuracy and reliability than finite element method in analyzing models with Rayleigh damping. Such method is also applied to complex structures such as typical micro-electro-mechanical system–based functionally graded magneto-electro-elastic energy harvester. Hence, ICS-FEM can be a powerful tool for transient problems of functionally graded magneto-electro-elastic models with damping which is of great value in designing intelligence structures.

scholarly journals The Influence of Valve-Pump Weight Ratios on the Dynamic Response of Leaking Valve-Pump Parallel Control Hydraulic Systems

2018 ◽  
Vol 8 (7) ◽  
pp. 1201 ◽  
Author(s):  
Haigang Ding ◽  
Jiyun Zhao ◽  
Gang Cheng ◽  
Steve Wright ◽  
Yufeng Yao
Keyword(s):  
Dynamic Response ◽  
Hydraulic System ◽  
Weight Ratio ◽  
Open Loop ◽  
Hydraulic Systems ◽  
Variable Speed ◽  
Weight Factors ◽  
Wide Range ◽  
Parallel Control ◽  
Valve Control

A new leaking valve-pump parallel control (LVPC) oil hydraulic system is proposed to improve the performance of dynamic response of present variable speed pump control (VSPC) system, which is an oil hydraulic control system with saving energy. In the LVPC, a control valve is operating at leaking status, together with a variable speed pump, to regulate the system flow of hydraulic oil simultaneously. Therefore, the degree of valve control and pump control can be adjusted by regulating the valve-pump weight ratio. The LVPC system design, mathematical model development, system parameter and control performance analysis are carried out systematically followed by an experimental for validation process. Results have shown that after introducing the valve control, the total leakage coefficient increases significantly over a wide range with the operating point and this further increases damping ratios and reduces the velocity stiffness. As the valve-pump weight ratio determines the flow distribution between the valve and the pump and the weight factors of the valve and/or the pump controls determines the response speed of the LVPC system, thus if the weight factors are constrained properly, the LVPC system will eventually have a large synthetic open-loop gain and it will respond faster than the VSPC system. The LVPC will enrich the control schemes of oil hydraulic system and has potential value in application requiring of fast response.

scholarly journals Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Pan Cheng ◽  
Ling Zhang
Keyword(s):  
Asymptotic Expansion ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Boundary Integral Equations ◽  
Logarithmic Singularity ◽  
Nonlinear Problems ◽  
Boundary Integral ◽  
Convergence Theory ◽  
Mechanical Quadrature ◽  
Quadrature Methods

This paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods (MQMs) are presented to solve the nonlinear equations where the accuracy of the solutions is of three orders. According to the asymptotical compact convergence theory, the errors with odd powers asymptotic expansion are obtained. Following the asymptotic expansion, the accuracy of the solutions can be improved to five orders with the Richardson extrapolation. Some results are shown regarding these approximations for problems by the numerical example.

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