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Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering rotational inertia and Gravitational Forces

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Computer Modeling in Engineering & Sciences 2022年第6期131卷 1857-1882页

作者： Shuangxin He Chaoyang Wang Xuan Zhou Leiting Dong Satya N.Atluri School of Aeronautic Science and Engineering Beihang UniversityBeijingChina Department of Mechanical Engineering Texas Tech UniversityLubbockUSA

The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are ***,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the *** this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are *** using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary *** due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM *** numerical examples are presented to verify this approach and results are compared with benchmark solutions.

关键词： Symmetric Galerkin boundary element method rotational inertia gravitational force weak singularity stress intensity factor

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rotational inertial Physics in Non-Classical Thermoviscous Fluent Continua Incorporating Internal Rotation Rates

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Applied Mathematics 2022年第6期13卷 453-487页

作者： K. S. Surana J. K. Kendall School of Mechanical Engineering University of Kansas Lawrence Kansas USA

In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, SLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor;(ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integ

关键词： Non-Classical Continuum Mechanics Internal Rotation Rates Angular Velocities Angular Accelerations rotational inertia Balance of Moment of Moments Thermoviscous Fluent Continua

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Analysis of the dynamic performance of an electro-hydrostatic actuator and improvement methods

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Chinese Journal of Aeronautics 2018年第12期31卷 2312-2320页

作者： Zhihui LI Yaoxing SHANG Zongxia JIAO Yan LIN Shuai WU Xiaobin LI School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100083China Science and Technology on Aircraft Control Laboratory Beihang UniversityBeijing 100083China

As a kind of actuation mechanism for power-by-wire(PBW) actuation systems of more/all electrical aircraft, an electro-hydrostatic actuator(EHA) is a highly integrated local hydraulic actuation system. It is a volume control system consisting of a motor, a pump, an actuator, etc.,which has features of high efficiency and reliability. However, the poor dynamic characteristic is one of the main factors restricting its wide application in aircraft. In this paper, the reason for the poor dynamic characteristic of an EHA is revealed from the perspectives of the natural frequency characteristic and the power requirement, respectively. In other words, the insufficiency of the motor output power at a high frequency is the main factor causing the poor dynamic characteristic of the system, and methods which include increasing the maximum output torque of the motor, reducing the rotational inertia of the motor-pump group, and adopting a double-motorpump group configuration are proposed in this paper, by which the dynamic characteristic of the system can be improved. The feasibility of those methods are verified by simulations. Finally, the dynamic characteristic is tested on an EHA prototype, and results show that saturation of the output torque of the motor is the main factor restricting the dynamic characteristic of the EHA system.

关键词： Dynamic characteristic Motor-pump group Power requirement rotational inertia

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