NEW CLOSED-FORM ANALYTICAL SOLUTIONS OF THE DISCRETE COAGULATION EQUATION WITH SIMULTANEOUS EVAPORATION AND THEIR USE FOR VALIDATION OF SECTIONAL SOLUTIONS

1993 ◽  
Vol 3 (2) ◽  
pp. 223-248 ◽  
Author(s):  
Yoram Tambour ◽  
Savely Khosid
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Coagulation Equation

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

Closed-form solutions of an elliptical crack subjected to coupled phonon–phason loadings in two-dimensional hexagonal quasicrystal media

2018 ◽  
Vol 24 (6) ◽  
pp. 1821-1848 ◽  
Author(s):  
Yuan Li ◽  
CuiYing Fan ◽  
Qing-Hua Qin ◽  
MingHao Zhao
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Elliptical Crack ◽  
Two Dimensional ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Crack Problems

An elliptical crack subjected to coupled phonon–phason loadings in a three-dimensional body of two-dimensional hexagonal quasicrystals is analytically investigated. Owing to the existence of the crack, the phonon and phason displacements are discontinuous along the crack face. The phonon and phason displacement discontinuities serve as the unknown variables in the generalized potential function method which are used to derive the boundary integral equations. These boundary integral equations governing Mode I, II, and III crack problems in two-dimensional hexagonal quasicrystals are expressed in integral differential form and hypersingular integral form, respectively. Closed-form exact solutions to the elliptical crack problems are first derived for two-dimensional hexagonal quasicrystals. The corresponding fracture parameters, including displacement discontinuities along the crack face and stress intensity factors, are presented considering all three crack cases of Modes I, II, and III. Analytical solutions for a penny-shaped crack, as a special case of the elliptical problem, are given. The obtained analytical solutions are graphically presented and numerically verified by the extended displacement discontinuities boundary element method.

Generalized Couette Flow of a Third-Grade Fluid with Slip: The Exact Solutions

2010 ◽  
Vol 65 (12) ◽  
pp. 1071-1076 ◽  
Author(s):  
Rahmat Ellahi ◽  
Tasawar Hayat ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Closed Form ◽  
Analytical Solutions ◽  
Present Note ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Flow Problems ◽  
Grade Fluid

The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form.

Assessment of Aided-INS Performance

2011 ◽  
Vol 65 (1) ◽  
pp. 169-185 ◽  
Author(s):  
Itzik Klein ◽  
Sagi Filin ◽  
Tomer Toledo ◽  
Ilan Rusnak
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Navigation Systems ◽  
Inertial Navigation Systems ◽  
Closed Form Solutions ◽  
Land Vehicles ◽  
Error Covariance ◽  
Model Dependency ◽  
Error State ◽  
Insight Into

Aided Inertial Navigation Systems (INS) systems are commonly implemented in land vehicles for a variety of applications. Several methods have been reported in the literature for evaluating aided INS performance. Yet, the INS error-state-model dependency on time and trajectory implies that no closed-form solutions exist for such evaluation. In this paper, we derive analytical solutions to evaluate the fusion performance. We show that the derived analytical solutions manage to predict the error covariance behavior of the full aided INS error model. These solutions bring insight into the effect of the various parameters involved in the fusion of the INS and an aiding sensor.

Analysis of transient amplification for a torsional system passing through resonance

2014 ◽  
Vol 229 (13) ◽  
pp. 2341-2354 ◽  
Author(s):  
Laihang Li ◽  
Rajendra Singh
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Classical Problem ◽  
Peak Frequency ◽  
Empirical Formulas ◽  
Closed Form Solutions ◽  
Analytical Approximations ◽  
Numerical Predictions ◽  
Prior Literature ◽  
Run Up

The classical problem of vibration amplification of a linear torsional oscillator excited by an instantaneous sinusoidal torque is re-examined with focus on the development of new analytical solutions of the transient envelopes. First, a new analytical method in the instantaneous frequency (or speed) domain is proposed to directly find the closed-form solutions of transient displacement, velocity, and acceleration envelopes for passage through resonance during the run-up or run-down process. The proposed closed-form solutions are then successfully verified by comparing them with numerical predictions and limited analytical solutions as available in prior literature. Second, improved analytical approximations of maximum amplification and corresponding peak frequency are found, which are also verified by comparing them with prior analytical or empirical formulas. In addition, applicability of the proposed analytical solution is clarified, and their error bounds are identified. Finally, the utility of analytical solutions and approximations is demonstrated by application to the start-up process of a multi-degree-of-freedom vehicle driveline system.

Closed-form analytical solutions incorporating pumping and tidal effects in various coastal aquifer systems

2014 ◽  
Vol 69 ◽  
pp. 1-12 ◽  
Author(s):  
Chaoyue Wang ◽  
Hailong Li ◽  
Li Wan ◽  
Xusheng Wang ◽  
Xiaowei Jiang
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Coastal Aquifer ◽  
Tidal Effects ◽  
Aquifer Systems

Analytical Solutions of Shock Fitting Equations for the Multishock Compaction of Die-Contained Powder Media

1992 ◽  
Vol 114 (1) ◽  
pp. 63-70
Author(s):  
Yukio Sano ◽  
Koji Tokushima ◽  
Yuji Inoue ◽  
Yoshihito Tomita
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Specific Volume ◽  
Linear Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Material Constants ◽  
The Difference ◽  
Volume Relation ◽  
Compaction Processes

In an earlier paper [4], two sets of equations which governed the processes of propagation of shock waves reflected from the punch and plug surfaces in a die-contained copper powder medium were presented. The pressure-specific volume relation included in the sets of equations was composed of three partial relations having different material constants. In the present paper the sets of equations are simplified by assuming that the pressure and specific volume at the front and back sides of the shock front are always related by the same material constants, and linear equations are obtained by introducing a further minor assumption into the simplified nonlinear equations included in the sets of equations. Two sorts of analytical solutions of the linear equations are obtained. One is a general-form solution, while the other is a closed-form solution. The general-form solution calculated is compared satisfactorily with the difference solution computed in the previous study, confirming that the assumption introduced into the simplified equations is minor. Furthermore, calculated characteristics of the general-form solution are revealed by the consideration of the simplified equations and the linear equations, giving greater insight into the compaction processes. The closed-form solution, which is obtained only for the propagation of the shock wave starting from the punch surface and returning from the plug surface, agrees well with the general-form solution.

Micropolar Modeling of Auxetic Chiral Lattices With Tunable Internal Rotation

2019 ◽  
Vol 86 (4) ◽  
Author(s):  
Hassan Bahaloo ◽  
Yaning Li
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Analytical Solutions ◽  
Elastic Moduli ◽  
Continuum Theory ◽  
Volume Element ◽  
Spring Stiffness ◽  
Stiffness Tensor ◽  
Micropolar Continuum ◽  
Fourfold Symmetry

Based on micropolar continuum theory, the closed-form stiffness tensor of auxetic chiral lattices with V-shaped wings and rotational joints were derived. Representative volume element (RVE) of the chiral lattice was decomposed into V-shape wings with fourfold symmetry. A unified V-beam finite element was developed to reduce the nodal degrees of freedoms of the RVE to enable closed-form analytical solutions. The elasticity constants were derived as functions of the angle of the V-shaped wings, nondimensional in-plane thickness of the ribs, and the stiffness of the rotational joints. The influences of these parameters on the coupled chiral and auxetic effects were systematically explored. The results show that the elastic moduli were significantly influenced by all three parameters, while Poisson's ratio was barely influenced by the in-plane thickness of the ribs but is sensitive to the angle of the V-shaped wings and the stiffness of the rotational springs. There is a transition region out of which the spring stiffness does not considerably affect the auxeticity and the overall lattice stiffness.

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