The present paper proposes a very simple one dimensional (1-D) model that accounts for the energy loss caused by the fluid dynamic losses occurring in the vaneless diffusers of centrifugal compressors and pumps. Usually, the present techniques to design turbomachines (pumps, compressors and turbines) emphasize numerical methods and their use is relatively complex because several parameters need to be chosen and a lot of time is required to perform the calculation. For this reason, it is relevant to perform an accurate preliminary design to simplify the numerical computation phase and to choose a very good initial geometry to be used for accelerating and improving the search for the definitive geometry. However, today 1-D modeling is based on the classical theory that assumes that the angular momentum is conserved inside a vaneless diffuser, although the flow evolution is considered as non-isentropic. This means that fluid-dynamic losses are taken into account only for what concerns pressure recovery, whereas the evaluation of the outlet tangential velocity incoherently follows an ideal behavior. Starting from such considerations, a new conservation law for the angular momentum is analytically derived, which incorporates the same fluid-dynamic losses modeled by the thermodynamic transformation law that is employed for correlating pressure recovery with enthalpy increase. Similar arguments hold for incompressible flows. Detailed and very accurate three-dimensional flow simulations are employed to analyze if the new model is capable of predicting the outlet tangential velocity more accurately than the classical theory. Results provided for both compressible (centrifugal compressors) and incompressible (centrifugal pumps) flows and for different inlet velocity profiles show a significant accuracy improvement of the new conservation law in the prediction of the outlet flow conditions when compared with the classical theory, thus demonstrating that the proposed model can be employed in the preliminary design of vaneless diffusers (i.e., in the estimation of the outlet diameter) more effectively than the classical ideal theory. Furthermore, the model is validated against industrial experimental campaigns. Even further experimental data, reported in a previous paper by the same authors, confirm the reliability of the employed approach.

The objective of this research is to find new equations for a novel phase-shifting method in digital photoelasticity. Some innovations are proposed. In terms of phase-shifting, only the analyzer is rotated, and the other equations are deduced by applying a new numerical technique instead of the usual algebraic techniques. This approach can be used to calculate a larger sequence of images. Each image represents a pattern and a measurement of the stresses present in the object. A reduction in the difference between the theoretical and experimental values of stresses was obtained by increasing the number of images in the equations for calculating phase. Every photographic image has errors and random noise, but the uncertainties due to these effects can be reduced with a larger number of observations.

The goal of this study was to investigate analytically the buckling phenomena of slender beam structures embedded in an elastic medium. In such cases, there is a possibility that spiral-shaped buckling modes can occur due to the restraining effect of the surrounding medium. As a result of analytical investigations, helical buckling occurs radically. Furthermore the pitch of the helix does not fluctuate as the radius of the helix increases. The interesting mechanical implications of the embedding effect are demonstrated by the theoretical approach established in this study.

The contribution is devoted to formulate an averaged mathematical model describing the dynamic behaviour of the composite annular plates resting on elastic heterogeneous foundation with two foundation modules. The plates are made of two-phased, functionally graded — type composites. In contrast to most of the papers in which material properties vary through the plate thickness, in the presented study we have dealt with the plate and foundation in which effective properties vary in a radial direction of the plate. The formulation of the macroscopic mathematical model for the analysis of the dynamic behaviour of these plates will be based on the tolerance averaging technique (Woźniak, Michalak, Jędrysiak, [ed]). This averaging method is an alternative to known asymptotic homogenization. The general results of the contribution will be illustrated by the analysis of free vibrations of the composite plates on heterogeneous foundation. The results obtained from the tolerance model were compared with the results obtained from FEM. There were compared the first four natural frequencies. A good consistency of the results from both methods was obtained.

We present an exact analysis of axisymmetric bending of circular plates according to elasticity theory. On the basis of Hamiltonian state space approach, a rigorous solution of the problem is determined by means of separation of variables and symplectic eigenfunction expansion in a systematic way. The thickness effect on bending of circular plates and the applicability of the classical plate solutions for the problem are evaluated accordingly.

In the present study, a closed-form analytical solution for the steady-state creep stresses of rotating thick cylindrical pressure vessels made of functionally graded materials (FGMs) is carried out. Norton's law governs the creep response of the material. Exact solutions for stresses and strain rate are obtained under the plane strain condition. How different material parameters involved in Norton's law affect radial and circumferential stresses together with the equivalent strain rate in rotating thick-walled cylindrical vessels under internal pressure is investigated. The result obtained shows that the property of FGMs has a significant influence on the equivalent creep strain rate and stresses distributions along the radial direction.

A multitude of researchers have utilized a variety of techniques to formulate the stresses and deformations caused by volume misfit inclusions in infinite host media. Few of such techniques can also be extended to derive solutions for inclusions in a half space. In this manuscript we present a novel computational method for determining the elastic fields of two and three-dimensional inclusions of arbitrary shape in an infinite host matrix. The misfit strain is treated by a distribution of prismatic dislocation loops. A systematic numerical assessment illustrates that the discretization can yield excellent agreement with existing analytical solutions for certain particle geometries. This method is then further developed to solve for two-dimensional problems in a half space.

The growth of the size of cache and the number of processor cores in modern CPUs is the major factor in advancing the computing performance of modern machines. The effect of CPU cache size in multicore computers on performance, however, has attracted little attention in lubrication and engineering analyses. In this study, the effect of cache size on the computational performance of two parallel iterative methods in solving two Reynolds equations is examined. Four computers, with CPU cache size from 4 to 40 MB and the number of processor cores from 4 to 16, were used. The sizes of the numerical grid were selected to simulate large gridwork (256 × 256) to small gridwork (2048 × 2048) tasks. It is found that the size of CPU cache is a major factor influencing the parallel efficiency in using the RBSOR method. On the other hand, the SPSOR method obtains much higher parallel efficiency than the RBSOR for medium-grained tasks, regardless of the size of CPU cache. The use of the SPSOR can, therefore, provide a much better parallel computing performance than the RBSOR in the cases of having a large number of grids or in a system with limited CPU cache.

It is known that the design problem of water distribution networks (WDNs) is an NP-hard combinatorial problem which cannot be easily solved using traditional mathematical numerical methods. On the other hand, fractional calculus, which is a generalization of the classical integer-order calculus, involves some interesting features such as having memory of past events. Based on the concept of fractional calculus, this paper proposes the use of a new version of heuristic shuffled frog leaping (SFL) algorithm for solving the optimal design problem of WDNs. In order to increase the convergence speed of the original SFL algorithm, a history of past events is added to the SFL updating formula. Moreover, some memeplexes of the original SFL method are altered to increase the diversification property of the SFL which helps the algorithm to avoid trapping in local optima. The new version of the SFL algorithm is called fractional succedaneum momentum shuffled frog leaping (FSSFL) method. The proposed FSSFL is applied for designing WDNs. Four illustrative and examples are presented to show the efficiency and superiority of the introduced FSSFL compared to the other well-known heuristic algorithms.

The boundary element method (BEM) is easier than the finite element method (FEM) on the viewpoint of the discretization of one dimension reduction rather than the domain discretization of finite element method. The disadvantage of BEM is the rank deficiency in the influence matrix, e.g., degenerate boundary, degenerate scale, spurious eigenvalues and fictitious frequencies, which do not occur in the FEM. The conventional BEM can not be straightforward applied to solve a problem which contains a degenerate boundary without decomposing the domain to multi-regions. A hypersingular integral equation is used to ensure a unique solution for the problem containing a degenerate boundary. By combining the singular and hypersingular equations, it’s termed the dual BEM due to its dual frame. Following the successful experience on the retrieval of information using the singular value decomposition (SVD) updating term and updating document, this technique is also used to extract out the degenerate-boundary information and the rigid-body information in the dual BEM. It is interesting to find that true information due to a rigid-body mode in physics is found in the right singular vector with respect to the corresponding zero singular value while the degenerate-boundary mode (geometry degeneracy) in mathematics is imbedded in the left singular vector with respect to the corresponding zero singular value. The role of the common right and left singular vectors of SVD for the four influence matrices in the dual BEM is also discussed in this paper. Two examples, a potential flow problem across a cutoff wall and a cracked bar under torsion were demonstrated to see the mathematical SVD structure of four influence matrices in the dual BEM.

A size-dependent dynamical model is suggested to investigate the vibrational characteristics of an Euler-Bernoulli micro/nanoscale beam. The strain gradient type of nonlocal elasticity is employed and a small intrinsic length scale parameter is considered in the theoretical model. A partial differential equation that governs transverse motion is derived and the corresponding ordinary differential equation and its dispersion relation are determined from the governing equation by the method of separation of variables. The problem is solved for several sets of strain gradient nonlocal boundary conditions by use of the eigenvalue method. These examples show that strain gradient nonlocality affects the natural frequencies of micro/nanoscale beams significantly. The initial axial force is also proved to play an important role in the vibrational behaviors of a micro/nanoscale beam. The critical compression and critical strain are derived and they are compared with some other approaches. The material constant in nonlocal elasticity theory can be determined by comparing the nonlocal theoretical results with molecular dynamic simulation and it is consistent with the estimation in previous work. Some further comments on the mechanisms of size dependence and physical meaning of micro/nanoscale parameter are presented. Comparisons of natural frequencies by nonlocal theory, classical theory, molecular dynamic simulation and surface effects are also constructed and they indicate the validity of the model developed in the present study.

The paper is to solve the problem of the response of stratified half-space subjected to triangularly distributed time-harmonic loadings on an axial symmetric area in the stratified half-space. Since the distributed area can be very small, the solution can be employed to deal with the problems of elastodynamics using the fundamental solution method. The advantage of the presented solution over Green function is that no singularity will occur in the presented solution. Some numerical results are given and some conclusions have been made. The presented solution is very efficient in computation.

The inverse problem of the Mei symmetry for nonholonomic systems with variable mass is studied. Firstly, the authors discuss the Mei symmetry of the holonomic system opposite to a nonholonomic system. Secondly, weak and strong Mei symmetries of a nonholonomic system are concluded through restriction equations and additional restriction equations. Thirdly, the relevant conserved quantity is deduced by means of the structure equation for the gauge function. Fourthly, the inverse problem of the Mei symmetry is obtained by the Noether symmetry. Finally, the paper offers an example to illustrate the application of the research result.

This paper provides a general solution for a crack embedded in multiply confocally elliptical layers in antiplane elasticity. In the problem, the elastic medium is composed of an inclusion, many confocally elliptical layers and the infinite matrix with different elastic properties. In addition, the remote loading is applied at infinity. The complex variable method and the conformal mapping technique are used. On the mapping plane, the complex potentials for the inclusion and many layers are assumed in a particular form with two undetermined coefficients. The continuity conditions for the displacement and traction along the interface between two adjacent layers are formulated and studied. By enforcing those conditions along the interface, the exact relation between two sets of two undetermined coefficients in the complex potentials for j-th layer and j + 1-th layer can be evaluated. From the traction free condition along the crack faces, the correct form of the complex potential for the cracked inclusion is obtained. Finally, many numerical results are provided.

A new procedure for simulating the active lateral force (Pa) is proposed for clays with anisotropic spatially variable undrained shear strength (su). With the proposed procedure, the Pa samples can be simulated without the use of the random field finite element method (RFEM). It requires only simple algebraic calculations and chart checking. Two retaining wall examples with isotropic or anisotropic random field are used to demonstrate the effectiveness of the proposed procedure.

A calculation model is put forward to analyze the interfacial response of an elastic frictionless punch, pressed normally into a half-plane, and subject to bending moment throughout this paper to observe the important effect that different normal loads and bending moments on the contact pressure distribution and contact deformation. Results for the detailed considerations have been given to the specific different cases of ηc. A characteristic response of the punch to a surplus bending moment has been found. The small differences can be observed between both methods show characteristic features of the FEM model and the theoretical model. The presented numerical results illustrate the influences of the normal load and bending moment on the contact stresses. The results obtained can be used to analyze the crack nucleation in fretting when the punch is acted upon by the normal force and the bending moment.

The present paper is concerned with an in-depth study of the effects of rotation, two-temperature parameter and voids on the magneto-thermoelastic interactions in a homogeneous, isotropic, generalized half-space with gravity field. The formulation is applied within the frame-work of two-temperature generalized thermoelasticity based on the hyperbolic heat conduction model with one relaxation time. Using normal mode analysis technique for the physical variables appearing in the governing equations, we get the analytical expressions for displacement components, stress, thermodynamic temperature, conductive temperature and change in volume fraction field. The general solution obtained is then applied to a specific problem of an infinite half-space having isothermal boundary subjected to mechanical load. Variations of the considered variables through the vertical distance are illustrated graphically.

Common materials, ranging from natural wood to modern composites, have been recognized as ortho-tropic materials. The elastic properties of such materials are governed by nine elastic constants. In this paper the complete set of Green's functions for an infinite medium and a half space is given, which were not reported completely before. Analytic expressions for the infinite Green's functions are derived through the explicit form of the sextic equation given explicitly. For an orthotopic half space, the Green's function is derived by a superposition method. The mathematical concept is based on the addition of a complementary term to the Green's function in an orthotropic infinite domain to fulfill the boundary condition on the free surface. Both solutions are illustrated in certain directions to demonstrate the nature of orthotropy.

This study examined the critical buckling characteristics of hydrostatically pressurized double-walled complete spherical shells. An analytical model based on small deflection thin shell theory is presented; the equations are solved in conjunction with variational principles. Axisymmetric and inextensional assumptions are not initially used in the exact formulation. This approach therefore avoids any discussion about the validity of the solution and allows the model to be extended to cover more generic nonaxisymmetric cases with relative ease. The analytical results are presented using illustrative buckling modes. Based on the developed formulation, only axisymmetric eigenmodes were found to occur despite the inclusion of the effect of interactions between outer and inner shells. Critical modes that are symmetric or antisymmetric about the equator may be determined depending on the combination of the stiffness connecting the outer and inner shells and the radius-to-wall thickness ratios.

The accurate and effective prediction of the failure for an inelastic structure, such as a solder joint in an electronic chip packaging, remains a current issue. Subjected to sub-critical cyclic loading, the solder can undergo fatigue cracks, leading to the failure of the whole system after a certain number of power cycles. In this paper, a model for describing the viscoplastic behavior of the solder material under power cycling is implemented in the finite element code Abaqus and a continuum damage procedure is used for lifetime prediction. Damage initiation criterion and damage evolution law, based both on the inelastic strain energy per stabilized cycle as proposed by Darveaux, are used in conjunction with the direct cyclic procedure available in Abaqus. This latter technique allows reducing the considerable computation time needed to obtain the stabilized states during the repetitive loading cycles.