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In this study, we conducted a theoretical analysis of thermal stress around an arbitrarily shaped hole in a thermoelectric material under electric current density and energy flux loading. Based on complex variable methods, conformal mapping, and analytical continuation theorem, the exact solutions of the thermal stress around a hole were obtained for the Seebeck coefficient and electric and heat conductivity. Based on the conversion efficiency equation of thermoelectric materials, higher electrical conductivity and lower heat conductivity should be selected to achieve an optimal design. The theoretical results indicated that higher electrical conductivity could reduce the thermal stress around the hole. However, energy flux and thermal stress concentration might be generated around the adiabatic hole due to the presence of a matrix with lower heat conductivity. Hence, thermoelectric materials with lower thermal conductivity should be selected carefully to avoid premature failure around the hole caused by thermal stress concentration. Finally, we also obtained and discussed the stress intensity factors of a hypocycloid-type crack.

The interaction between a screw dislocation and an oblique edge crack in a semi-infinite piezoelectric medium under remote anti-plane mechanical and in-plane electrical loadings is studied in this article. The screw dislocation suffers a finite discontinuity in the displacement and electric potential across the slip plane. The dislocation also has a line force and a line charge along its core. In the framework of linear piezoelectricity theory, the analytical solutions are derived from the complex variable and Schwarz–Christoffel transformation. Furthermore, the electric field, stress field, generalized stress intensity factor, image force and crack extension force are formulated exactly. Numerical calculations are then given graphically for studying the effects of crack length, crack angle and load position on these electric mechanical parameters. Besides, the dislocation solutions proposed here can be served as Green’s functions for the analyses of corresponding piezoelectric cracking or distributed loading problems.

Double-layer heterogeneous photoresist method will be used firstly to obtain the round photoresist column with two layers of different photoresists. Since both photoresists are the positive-type, the exposure is only required once. During the thermal reflow processing, the upper photoresist layer (AZ-4620 and nanomagnetic powder mixture) reaches the glass transition temperature, which is transformed from a glassy state into a rubbery state. Since the glass transition temperature of the lower photoresist layer (AZ-5214E) is higher than the temperature of thermal reflow, the lower photoresist layer is still able to maintain its solid state. The lower layer creates a round base during the thermal reflow process, and then subjected to an appropriate magnetic field. The base can not only restrict the bottom shape of the liquid photoresist to a round shape but also prevent the sliding of liquid photoresist during the thermal reflow process, so the tilted microlens array can be obtained. We can vary the strength of magnetic field to control the oblique angle of the tilted microlens.

This study presents a novel fabrication method for asymmetric microlens arrays for light control films that increase the efficiency of liquid crystal displays used to collect lateral light sources and improve the brightness within the angle of view. Initially, the pattern allows exposure through the placement of a photoresist-coated substrate on an inclined fixture. An inclined photoresist column array with a round cross section is constructed using a photolithography technique. During the incomplete thermal reflow processing, only the surface part of the photoresist column reaches the glass transition temperature (Tg) and is transformed from a glassy state into a rubbery state. In order to minimize the structural surface energy and reduce the surface area, the surface of the inclined photoresist column forms the shape of a lens. With proper control of the thermal reflow temperature and processing time, the photoresist at the base maintains its original inclination and glassy state, because it does not re...

A simple and rapid fabrication method for a semiellipsoid microlens array has been proposed in this study. Low-loss coupling can be achieved between a laser diode and a single-mode fiber. The single-mode fiber is tipped with a newly developed semiellipsoid microlens in this technique. Average array coupling loss is as low as 15%. Two different photoresist layers are firstly coated on a silicon wafer in sequence. After the lithography process, the elliptical photoresist column with two different photoresists can be obtained. During the thermal reflow processing, upper photoresist layer (AZ-4620) reaches the glass transition temperature (T"g), which is transformed from a glassy state into a rubbery state. Due to their high surface tension, liquid photoresist tend to minimize the structural energy and reduce their surface trying to achieve a lens shape. Since the glass transition temperature of lower photoresist layer (AZ-5214E) is higher than the temperature of thermal reflow, the lower photoresist layer still maintained solid state. The elliptical base can precisely define the bottom of the liquid photoresist as an elliptical shape. Electroforming technology is then used to convert the photoresist patterns into a metallic mold for PDMS semiellipsoid microlens. A coupling efficiency of up to 85% can be obtained using a semiellipsoid microlens fabricated by our proposed method.

This paper analyzes the antiplane problem of a finite piezoelectric wedge subjected to concentrated loads. The piezoelectric wedge is assumed to be transversely isotropic with the poling direction along the x 3 direction. The concentrated loads considered here involve screw dislocations with the Burgers vectors parallel to the poling direction. In addition, a line force and a line charge are applied at the core of the dislocation. Four different boundary conditions on the radial edge and the circular edge are investigated and the concentrated loads can be located in the full domain of the finite wedge. The analytical derivation is based on the complex variable, analytical continuation and the conformal mapping methods. The derived complex potentials show that the stress and electric displacement fields display r 1 − λ type of singularity near the wedge crack-tip when the wedge angle is larger than π . The obtained solutions then are used to calculate the electric-elastic fields and the crack-tip stress and electric displacement intensity factors. The results are further degenerated to several specific cases and are agreed well with existing ones.

The electro-elastic stress investigation on the interaction between a screw dislocation and a half-plane trimaterial composite composed of three bonded dissimilar transversely isotropic piezoelectric materials is analyzed in the framework of linear piezoelectricity. Each layer is assumed to have the same material orientation with x3 in the poling direction. The dislocations are characterized by a discontinuous displacement and electric potential across the slip plane and are subjected to a line force and a line charge at the core. Based on the complex variable and the method of alternating technique, the solution of electric field and displacement field is expressed in terms of explicit series form. The solutions derived here can be applied to a variety of problems, for example, a half-plane bimaterial, a quarter-plane bimaterial, a quarter-plane material and a rectangular strip etc. Numerical results are provided to show the influences of the material combinations and geometric configurations on the electro-elastic fields and image force calculated through the generalized Peach-Koehler formula. The solutions proposed here can be served as Green’s functions for the analyses corresponding piezoelectric cracking problems.

The interaction problem between a screw dislocation and a piezoelectric fiber composite with a semi-infinite wedge crack is investigated in this paper. The piezoelectric media are assumed to be transversely isotropic with the poling direction along the x 3 direction. The screw dislocation considered here involves a Burgers vector parallel to the poling direction with a line force and a line charge being applied at the core of the dislocation. Both cases of the screw dislocation located at the matrix and inclusion are observed. The analytical derivation is based on the complex variable and the conformal mapping methods. The exact solutions are obtained to calculate the forces on the dislocation and the crack-tip stress and electric displacement intensity factors. Based on these results, the anti-shielding and shielding effects for different loadings, material combinations, and geometric configurations are discussed in detail.

In this paper, the interaction of a generalized screw dislocation with multiple circular inclusions perfectly bonded to an unbounded matrix under remote magnetoelectromechanical loadings is dealt with. The analytical solutions of electric field, magnetic field and displacement field either in the inclusions or the matrix are obtained by use of the complex variable method. The image force acting on the magnetoelectric screw dislocation is calculated by using the generalized Peach-Koehler formula. Finally, the influence of material combinations on the image force is examined for several practical examples. The obtained solutions can be used as Green's functions for the analysis of the corresponding magnetoelectric crack problem.

This paper analyzes a coated inclusion of arbitrary shape embedded in an infinite plate subjected to anti-plane mechanical and in-plane electrical loadings. Based on the methods of complex variable, conformal mapping, Faber series and Laurent series, the complex potential for each component can be expressed in series form with unknown coefficients. The continuity conditions of the interfaces are used to build up a set of linear equations to determine the unknown coefficients. The exact solutions are obtained after the complex potentials are solved. By truncating the infinite system of linear equations at finite N terms, some numerical examples are provided to show the effect of the material mismatch and the shape of inclusion on the interfacial stress and elastic field. The accuracy of the linear systems is also discussed in the article.

Within the framework of the linear theory of magnetoelectroelasticity, the problem of a circular layered inclusion interacting with a generalized screw dislocation under remote anti-plane shear stress and in-plane magnetoelectric loads is investigated in this paper. The generalized dislocation can be located either in the matrix or in the circular layered inclusion. The layers are coaxial cylinders of annular cross-sections with arbitrary radii and different material properties. Using complex variable theory and the alternating technique, the solution of the present problem is expressed in terms of the solution of the corresponding homogeneous medium problem subjected to the same loading. Some numerical results are provided to investigate the influence of material combinations on the shear stress, electric field, magnetic and image force. These solutions can be used as Green's functions for the analysis of the corresponding magnetoelectric crack problem.

Within the framework of the linear theory of piezoelectricity, the problem of circularly cylindrical layered media under anti-plane deformations and in-plane electric fields is considered and solved in this paper. The layers are coaxial cylinders of annular cross-sections with arbitrary radii and different material properties. Based on the complex variable theory and the method of alternating technique, the solution of the present problem is expressed in terms of the solution of the corresponding homogeneous problem subjected to the same loading. Stress and electric field concentrations which are dependent on the mismatch in the material constants, the location of singularities and the magnitude of electromechanical loadings are studied in detail. In the course of these developments, it is discovered that certain types of inclusions do not disturb a uniform anti-plane shear and a uniform in-plane electric field.

This paper presents a novel efficient procedure to analyze the two-phase confocally elliptical inclusion embedded in an unbounded matrix under antiplane loadings. The antiplane loadings considered in this paper include a point force and a screw dislocation or a far-field antiplane shear. The analytical continuation method together with an alternating technique is used to derive the general forms of the elastic fields in terms of the corresponding problem subjected to the same loadings in a homogeneous body. This approach could lead to some interesting simplifications in solution procedures, and the derived analytical solution for singularity problems could be employed as a Green's function to investigate matrix cracking in the corresponding crack problems. Several specific solutions are provided in closed form, which are verified by comparison with existing ones. Numerical results are provided to show the effect of the material mismatch, the aspect ratio, and the loading condition on the elastic field due to the presence of inhomogeneities.

In this work, the analytical solution of a fundamental problem of heat conduction in anisotropic medium is derived. The steady-state temperature field in an anisotropic trimaterial subject to an arbitrary heat source is analyzed. “Trimaterial” denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. The method of analytical continuation is applied across the two parallel interfaces in order to derive the trimaterial solution in a series form from the corresponding homogeneous solution. A variety of problems, e.g., bimaterial, a finite thin film on a semi-infinite substrate, and a finite strip, can be analyzed as special cases of the present study. The numerical results of the temperature distributions for some practical examples are provided in graphic form and discussed in details.

A new fabrication method for a tilted microlens array for light control films was developed to increase the efficiency of a liquid crystal display so that lateral light sources are collected and the dazzling light problem at certain viewing angles is improved. The thermal reflow with two layers of different photoresists is used to fabricate the tilted microlens array in this study. After the lithography process, the round photoresist column with two layers of different photoresists can be obtained. During the thermal reflow processing, the upper photoresist layer (AZ-4620) reaches the glass transition temperature, which is transformed from a glassy state into a rubbery state. Since the glass transition temperature of the lower photoresist layer (AZ-5214E) is higher than the temperature of thermal reflow, the lower photoresist layer is still able to maintain its solid state. The lower layer creates a round base during the thermal reflow process. The experimental results show that the photoresist mold of tilted microlens may be produced under gravity by inverting and tilting the substrate during the thermal reflow process. After the wafer is placed inversely and obliquely, the base can not only restrict the bottom shape of the liquid photoresist to a round shape but also prevent the sliding of liquid photoresist during the thermal reflow process. Compared with the conventional thermal reflow without a base, the photoresist base is relatively reliable and effective in preventing lenses from sliding.

We present a new semiellipsoid microlens fabrication method using the lift-off and alignment exposure processes. The lift-off method is used to create an elliptical base before the thermal reflow process. During the photoresist thermal reflow process, the elliptical base can precisely define the bottom shape of the liquid photoresist, and fabricate the semiellipsoid microlens array with a large height and small radius of curvature. The prolate spheroid approximation method is developed to estimate the thickness of the elliptic photoresist column required by the semiellipsoid microlens of a certain height, with the error being controlled within ±3%. Electroforming technology is then used to convert the photoresist patterns into a metallic mold for a PDMS ellipsoidal microlens. The experiment results show that the geometries of a semiellipsoid microlens can be accurately defined by three parameters: the length of the major axis of the elliptical base, the length of the minor axis of the elliptical base and the thickness of the elliptical photoresist column. The proposed fabrication method facilitates mass production to achieve a high-yield and high-coupling semiellipsoid microlens that is suitable for use in commercial fiber transmission systems

We present a new semiellipsoid microlens fabrication method that controls the printing gap in the UV lithography process without thermal reflow. The UV proximity printing method can precisely control the curvature radius ratio of the semiellipsoid microlens in the fabrication process. The proposed fabrication method facilitates mass production to achieve a high-yield and high-coupling semiellipsoid microlens that is suitable to be used in commercial fiber transmission systems. A semiellipsoid microlens can be tipped on a single-mode fiber end to improve power coupling efficiency from laser diodes. The semiellipsoid microlens allows increasing the fiber spot size and numerical aperture. It is very important to control the geometric parameters in the assembly procedure to increase the optical coupling efficiency between the laser diode and single-mode fiber. Wide misalignment tolerance, low loss, and low manufacturing cost could be achieved by the proposed fabrication method. The theoretical model is first developed to predict the optical coupling efficiency for various microstructure geometries of semiellipsoid microlens and assembly parameters in this study. Then, the Taguchi method is applied to obtain the optimal geometric parameters setting. The results show that optical coupling efficiency could be significantly improved by using the optimal geometric parameters setting.

The sequential neural-network approximation and orthogonal array (SNAOA) were used to shorten the cooling time for the rapid cooling process such that the normalized maximum resolved stress in silicon wafer was always below one in this study. An orthogonal array was first conducted to obtain the initial solution set. The initial solution set was treated as the initial training sample. Next, a back-propagation sequential neural network was trained to simulate the feasible domain to obtain the optimal parameter setting. The size of the training sample was greatly reduced due to the use of the orthogonal array. In addition, a restart strategy was also incorporated into the SNAOA so that the searching process may have a better opportunity to reach a near global optimum. In this work, we considered three different cooling control schemes during the rapid thermal process: (1) downward axial gas flow cooling scheme; (2) upward axial gas flow cooling scheme; (3) dual axial gas flow cooling scheme. Based on the maximum shear stress failure criterion, the other control factors such as flow rate, inlet diameter, outlet width, chamber height and chamber diameter were also examined with respect to cooling time. The results showed that the cooling time could be significantly reduced using the SNAOA approach.