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Frictional sliding contact problems between laterally graded orthotropic half-planes and a flat rigid stamp are investigated. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members.

The solution procedure is based on a finite element (FE) approach which is conducted with an efficient FE analysis software ANSYS. The spatial gradations of the orthotropic stiffness constants through the horizontal axis are enabled utilizing the homogeneous FE approach. The Augmented Lagrangian contact algorithm is used as an iterative non-linear solution method in the contact analysis.

The accuracy of the proposed FE solution method is approved by using the comparisons of the results with those computed using an analytical technique. The prominent results indicate that the surface contact stresses can be mitigated upon increasing the degree of orthotropy and positive lateral gradations.

One can infer from the literature survey that, the contact mechanics analysis of orthotropic laterally graded materials has not been investigated so far. In this study, an FE method-based computational solution procedure for the aforementioned problem is addressed. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members. Additionally, this study provides some useful points related to computational contact mechanics analysis of orthotropic structures.

The purpose of this paper is to investigate the problem of fracture of construction by solution of several mixed unsteady boundary value problems of elasticity, determination of stress intensity factors and concentration of stresses near edges of cracks and by numerical calculations of them obtained by explicit formulae.

The main methods of solution are integral transformations of Laplace and Fourier, method of Winner‐Hopf system solution by avoiding the singularities of coefficients of their matrices and factorization of them using numerical solution of the same order system of Fredholm integral equations. The solution for stresses is obtained in originals by effective Smirnov‐Sobolev form. The obtained integrals for stress intensity coefficients are calculated for considered cases of plane and anti‐plane problems of cracks, and for more complex space problem of crack are carried out all mentioned analytical investigations, including derivation of stresses distributions formulae near crack edge.

These analytic and numerical methods based on dynamic elasticity approximation on account of singularities near cracks edge allow precise calculation of the possibility and character of fracture of media under any loading of rather complex type.

Results can be useful for investigation of constructions responsibility. The developed mathematical methods are original and modern, using all actual effective methods of investigation of solutions of linear system of equations with three and four independent variables for complex initial, boundary value problems.

Control-signal-to-output-voltage transfer function of the conventional boost converter has at least one right-half plane zero (RHPZ) in the continuous conduction mode which can restrict the open-loop bandwidth of the converter. This problem can complicate the control design for the load voltage regulation and conversely, impact on the stability of the closed-loop system. To remove this positive zero and improve the dynamic performance, this paper aims to suggest a novel boost topology with a step-up voltage gain by developing the circuit diagram of a conventional boost converter.

Using a transformer, two different pathways are provided for a classical boost circuit. Hence, the effect of the RHPZ can be easily canceled and the voltage gain can be enhanced which provides conditions for achieving a smaller working duty cycle and reducing the voltage stress of the power switch. Using this technique makes it possible to achieve a good dynamic response compared to the classical boost converter.

The observations show that the phase margin of the proposed boost converter can be adequately improved, its bandwidth is largely increased, due to its minimum-phase structure through RHPZ cancellation. It is suitable for fast dynamic response applications such as micro-inverters and fuel cells.

The introduced method is analytically studied via determining the state-space model and necessary criteria are obtained to achieve a minimum-phase structure. Practical observations of a constructed prototype for the voltage conversion from 24 V to 100 V and various load conditions are shown.

This paper aims to introduce a new class of entire functions whose zeros (z_k)_k≥1 satisfy ∑_k=1^∞Im z_k=O(1).

This is done by means of a Ritt's formula which is used to prove that every partial sum of the Riemann Zeta function, ζ_n(z):=∑_k=1ⁿ1/k^z, n≥2, has zeros (s_nk)_k≥1 verifying ∑_k=1^∞Re s_nk=O(1) and extending this property to a large class of entire functions denoted by A_O.

It is found that this new class A_O has a part in common with the class A introduced by Levin but is distinct from it. It is shown that, in particular, A_O contains every partial sum of the Riemann Zeta function ζ_n(iz) and every finite truncation of the alternating Dirichlet series expansion of the Riemann zeta function, T_n(iz):=∑_k=1ⁿ(−1)^k−1/k^iz, for all n≥2.

With the exception of the n=2 case, numerical experiences show that all zeros of ζ_n(z) and T_n(z) are not symmetrically distributed around the imaginary axis. However, the fact consisting of every function ζ_n(iz) and T_n(iz) to be in the class A_O implies the existence of a very precise physical equilibrium between the zeros situated on the left half‐plane and the zeros situated on the right half‐plane of each function. This is a relevant fact and it points out that there is certain internal rule that distributes the zeros of ζ_n(z) and T_n(z) in such a way that few zeros on the left of the imaginary axis and far away from it, must be compensated with a lot of zeros on the right of the imaginary axis and close to it, and vice versa.

The paper presents an original class of entire functions that provides a new point of view to study the approximants and the alternating Dirichlet truncations of the Riemann zeta function.

Thermal fractures initiated under cooling at the surfaces of a 2-D or 3-D structure propagate, arrest and coalesce, leading to its structural failure and material-property changes, while the same processes can happen in the rock mass between parallel hydraulic fractures filled with cold fluid, leading to enhanced fracture connectivity and permeability.

This study used a 2-D plane strain fracture model for mixed-mode thermal fractures from two parallel cooling surfaces. Fracture propagation was governed by the theory of linear elastic fracture mechanics, while the displacement and temperature fields were discretized using the adaptive finite element method. This model was validated using two numerical benchmarks with strong fracture curvature and then used to simulate the propagation and coalescence of thermal fractures in a long rock mass.

Modeling results show two regimes: (1) thermal fractures from a cooling surface propagate and arrest by following the theoretical solutions of half-plane fractures before the unfractured portion decreases to 20% rock-mass width and (2) some pairs of fractures from the opposite cooling surfaces tend to eventually coalesce. The fracture coalescence time is in a power law with rock-mass width.

These findings are relevant to both subsurface engineering and material engineering: structure failure is a key concern in the latter, while fracture coalescence can enhance the connectivity of thermal and hydraulic fractures and thus reservoir permeability in the former.

A finite element mesh generator is described based on a conformal mapping which requires little more than the definition of boundary geometry to generate a mesh. The method is restricted to plane regions which are simply connected. The interior of a region containing a uniform mesh of regularly shaped 8‐node quadrilateral elements is mapped conformally to the physical domain with the result that bandwidth is automatically minimized and that smooth transitions are made between large and small elements. Although the procedure is not satisfactory for general applications, most common geometrical shapes can be modelled with meshes of good quality. The method is based primarily on boundary data but the user can specify a region of high mesh density. Examples are given to illustrate typical results.

Based on the governing equations of magneto‐electro‐elastic media, the general solutions in the case of distinct eigenvalues and is introduced and expressed in four harmonic functions. Then, the Green’s functions for point forces, point charge and point current acting in the interior of a two‐phase infinite magneto‐electro‐elastic plane in the case of distinct or multiple eigenvalues are given using the method of mirror image source.

A new algorithm for the inhomogeneous Boltzmann equation in one spatial and velocity dimension, based on the method of characteristics, is presented. Using the analytic solution to the Boltzmann equation along its characteristics, the solution to the classical transport problem in semiconducting structures within the relaxation time approximation for the collision integral is obtained iteratively. An n+nn+‐diode is studied numerically and the effects of ballastic electrons on low‐order moments are investigated.

The authors presents mathematical models of hysteretical relations of main magnetic parameters in pulse measuring procedures. Fragments of hysteresis loop specific for assessment of magnets as well as particular hysteresis parameters are discerned.

Conventional isolated dc–dc converters offer an efficient solution for performing voltage conversion with a large improved voltage gain. However, the small-signal analysis of these converters shows that a right-half-plane (RHP) zero appears in their control-to-output transfer function, exhibiting a nonminimum-phase stability. This RHP zero can limit the frequency response and dynamic specifications of the converters; therefore, the output voltage response is sluggish. To overcome these problems, the purpose of this study is to analyze, model and design a new isolated forward single-ended primary-inductor converter (IFSEPIC) through RHP zero alleviation.

At first, the normal operation of the suggested IFSEPIC is studied. Then, its average model and control-to-output transfer function are derived. Based on the obtained model and Routh–Hurwitz criterion, the components are suitably designed for the proposed IFSEPIC, such that the derived dynamic model can eliminate the RHP zero.

The advantages of the proposed IFSEPIC can be summarized as: This converter can provide conditions to achieve fast dynamic behavior and minimum-phase stability, owing to the RHP zero cancellation; with respect to conventional isolated converters, a larger gain can be realized using the proposed topology; thus, it is possible to attain a smaller operating duty cycle; for conventional isolated converters, transformer core saturation is a major concern, owing to a large magnetizing current. However, the average value of the magnetizing current becomes zero for the proposed IFSEPIC, thereby avoiding core saturation, particularly at high frequencies; and the input current of the proposed converter is continuous, reducing input current ripple.

The key benefits of the proposed IFSEPIC are shown via comparisons. To validate the design method and theoretical findings, a practical implementation is presented.