This paper presents a new computational strategy along with a computational and mathematical framework for computing non-weak numerical solutions of stationary and time dependent partial differential equations. This approach utilizes strong form of the governing differential equations (GDE) and least squares approach in constructing the integral form. This new proposed approach is applied to one dimensional transient gasdynamics equation in Eulerian frame of reference using ρ, u , T as dependent variables. The currently used finite element approaches seek convergence of a solution in a fixed order space by h , p , or hp -adaptive processes. The fundamental point of departure in the proposed approach is that we seek the convergence of the computed converged solution over the spaces of different orders containing the basis functions. With this approach, dramatically higher convergence rates than those obtained for h , p , or hp -processes are achievable and the sequence of progressively converged solutions over the spaces of progressively increasing order in fact converge to the strong solution (analytical or theoretical) of the partial differential equation. It is demonstrated using one-dimensional transient Navier-Stokes equations for compressible fluid flow in Eulerian frame of reference, that in the presence of physical diffusion and dissipation, our computed solutions have exactly the same characteristics as the strong solutions. Riemann shock tube is used as a model problem.

This paper presents formulations, computations and investigations of the solutions of class C 00 and C 11 for two dimensional viscoelastic fluid flows in u, v, p, τ ij p , τ ij s with Oldroyd-B constitutive model using p-version Least Squares Finite Element Formulation (LSFEF). The main thrust of the research work presented in the paper is to employ ‘right class of interpolations’ and the best computational strategy to establish: i) when does Oldroyd-B model begins to fail in simulating the correct physics of flow ii) when and why does the proposed computational process fail iii) is there a correlation between i) and ii). Fully developed flow between parallel plates and the stick-slip problems are used as model problems. The investigations presented in this paper reveal the following. a) The manner in which the stresses are non-dimensionalized significantly influences the performance of the iterative procedure of solving nonlinear algebraic equations. b) Solutions of the class C 00 are always the wrong class of solutions of GDEs in variables u, v, p, τ ij p and τ ij s and thus spurious. c) C 11 class of solutions are the right class of solutions of the GDEs in variables u, v, p, τ ij p and τ ij s . d) In the flow domains, containing sharp gradients of the dependent variables, conservation of mass is difficult to achieve at lower p-levels (worse for coarse meshes). e) An augmented form of GDEs are proposed that always ensure conservation of mass at all p-levels regardless of the mesh and the nature of the solution gradients. f) We demonstrate that Oldroyd-B model describes correct physics of dilute polymer solutions of constant viscosity only for a limited range of Deborah numbers. Beyond this range, the computed solutions are not in agreement with the flow physics (thus spurious) even though the proposed computational process works exceptionally well. g) Numerical studies with graded meshes and high p-levels presented in this paper are aimed towards establishing and demonstrating detail behavior of local as well as global nature of the computed 10 solutions, h) Various norms are proposed and tested to judge local and global dominance of elasticity or viscous behavior 1) New definitions are proposed for elongational (extensional) viscosity. The proposed definitions are more in conformity and agreement with the flow physics compared to currently used definitions j) A significant aspect and strength of our work is that we utilize straightforward p-version LSFEF with C 00 and C 11 type interpolations without linearizing GDEs and that SUPG, SUPG/DC, SUPG/DC/LS operators are neither needed nor used.

Fiber breakage occurring in fiber bundles of plain-woven glass fabric composites is investigated under tension/shear biaxial cyclic stress. The experimental results show an existence of the strong effect of biaxial stress ratio on fiber breakage and its accumulation. Under pure tension (uniaxial) loading, the variation of fiber breakage ratio with respect to loading cycles is divided into two stages in the longitudinal fiber bundles. In the first stage, the fiber breakage scarcely occurs. In the final stage, fibers in a fiber bundle are broken remarkably. Under the biaxial cyclic stress, the fiber breakage in the longitudinal fiber bundle is observed in initial fatigue stage. In the case of the biaxial stress with large shear stress component, the fiber breakage is also observed in the transverse fiber bundle. The fiber breakage is accelerated by the combined stress with large shear stress component, which is called the shear constraint effect.

The purpose of this study is to establish an Inside Temperature (IT) method for estimating temperatures in steady wave fronts in a thermoviscous material. A fundamental assumption that the material in the wave front, was approximately in an equilibrium state was used in this method. A further assumption that heat transport was neglected was used in the IT dQ=0 method, while in the IT IM method, the work done by the thermal stress was offset by heat transport. Two irreversible thermodynamic equations for the temperature in the wave front derived were connected with the Hugoniot function and the Mie-Grüneisen equation, respectively. To verify the efficacy of the IT method, three temperature distributions were estimated qualitatively using an equation for entropy including no assumption on heat transport, that including the assumption used in the IT dQ=0 method, and that in the IT IM method. These three distributions suggested that the temperatures were overestimated by the IT dQ=0 method, while the IT IM method was effective for shock compressions where the effect of viscosity was distinguished.

This paper presents a new theoretical and computational framework for computing solutions of right classes for laminated composites using 2D p-version least squares finite element formulation incorporating the correct physics of interlamina behavior. At the interface between two laminas of dissimilar materials we have continuity of displacements u, v, stresses σ yy , τ xy , and strain ε xx , while the stress σ xx and the strains ε yy and γ xy are discontinuous. Thus, a finite element formulation, incorporating the physics of laminate behavior, would require interpolation of u, v, ε xx , σ yy and τ xy instead of u, v, σ xx , σ yy and τ xy which is generally the case in most mixed formulations. In the p-version LSFEF presented here, we interpolate u, v and σ yy , τ xy (ε xx = ∂u/∂x is used to eliminate ε xx as a variable) using appropriate p-version interpolations which would ensure correct interlamina behavior of these components. When the mating lamina properties are different, interlamina discontinuity of σ xx , ε yy and γ xy is automatically generated due to dissimilar material properties of the laminas. In this formulation interlamina jumps in σ xx , ε yy and γ xy do not constitute singularities, hence mesh refinements and higher p-levels are not needed in the vicinity of inter-lamina boundaries. The major thrust of this paper is to construct interpolations for the dependant variables that are of right classes in appropriate spaces so that a sequence of converged solutions in these spaces may be computed which, when converged, would yield a numerical solution that has exactly the same characteristics (in terms of continuity and differentiability) as the analytical or theoretical (strong) solution.

Advanced Grid Stiffened composite structures are desirable building components for space flight vehicles because they provide enhanced stiffness yet are relatively low-cost, long-lasting, and light-weight. Analysis of a grid stiffened structure presents significant challenges. The stiffener design is discrete and involves a set of stiffener orientations which complicates the solution process. Most optimization algorithms only provide a single global optimum, while a designer would want to obtain all of the local minima that have performance close to the global optimum. As a preliminary to the optimization analysis, the bending stiffness of grid stiffened cylinders will be modeled analytically with in-plane loads. The model developed in this paper will be used in further research with a hybrid optimization algorithm to conduct the optimization analysis.

This paper presents formulations, computations and investigations of the solutions of classes C 00 and C 11 for two dimensional viscoelastic fluid flows in u, v, p, τ ij p , τ ij s with Giesekus constitutive model using p-version least squares finite element formulation (LSFEF). The main thrust of the research work presented in the paper is to employ ‘right classes of interpolations’ and the ‘best computational strategy’ 1) to obtain numerical solutions of governing differential equations (GDEs) for increasing Deborah numbers 2) to investigate the nature of the computed solutions with the aim of establishing limiting values of the flow parameters beyond which the solutions may be possible to compute, but may not be meaningful. The investigations presented in this paper reveal the following: a) The manner in which the stresses are non-dimensionalized significantly influences the performance of the iterative procedure of solving non-linear algebraic equations. b) Solutions of the class C 00 are always the wrong class of solutions of GDEs in variables u, v, p, τ ij p and τ ij s and thus spurious. c) C 11 class of solutions are the right class of solutions of the GDEs in variables u, v, p, τ ij p and τ ij s . d) In the flow domains, containing sharp gradients of the dependent variables, conservation of mass is difficult to achieve at lower p-levels (worse for coarse meshes). e) An augmented form of GDEs are proposed that always ensure conservation of mass at all p-levels regardless of the mesh and the nature of the solution gradients. f) Stick-slip problem is used as a model problem. Dimensions, fluid properties and flow rates used correspond to MIT experiments [20]. We demonstrate that converged solutions are possible to compute for all flow rates reported in ref [20] and that the detailed examination of the solution characteristics reveals them to be in agreement with all the physics of the flow, g) Numerical studies with graded meshes and high p-levels presented in this paper are aimed towards establishing and demonstrating detail behavior of local as well as global nature of the computed solutions, h) Various norms are proposed and tested to judge local and global dominance of elasticity or viscous behavior i) New definitions are proposed for elongational (extensional) viscosity. The proposed definitions are more in conformity and agreement with the flow physics compared to currently use definitions j) A significant aspect and strength of our work is that we utilize straightforward p-version LSFEF with C 00 and C 11 type interpolations without linearizing GDEs and that SUPG, SUPG/DC, SUPG/DC/LS operators are neither needed nor used.

The solid-state welding method was applied under atmospheric conditions by using metal powder medium which was interposed in the space between the two solid bars of specimen (i.e., base metal), and was compressed longitudinally and simultaneously current was conducted to generate Joule thermal heat. Some fundamental data on the mechanical and metallurgical properties of the joint were obtained by using resistance welding. In the experiments, the specimen materials used as base metals in this study were pure aluminum, stainless steel and titanium bars of solid, and the powder media were aluminum, nickel and silicon powder. The mixed silicon powder medium increases electric resistance between base metals, moreover, to obtain mechanical properties. Four experiments were conducted with different specimen; The first experiment used two solid aluminum specimen bars with aluminum powder medium. The second, two solid aluminum specimen bars with mixed aluminum and nickel powder media. The third, two solid aluminum specimen bars with mixed nickel and silicon powder media. And the fourth, solid specimen were different materials and had relatively different melting points. Such as solid aluminum and stainless steel (SUS430) with mixed nickel and silicon powder media, and solid aluminum and titanium with mixed aluminum and nickel powder media. Data were obtained with the intent of optimizing the method using powder medium between a pair of solid sample specimen and observation, analysis and assessment were made with microscope. Scanning Electron Microscope (SEM), Energy Dispersive X-ray spectroscopy (EDX). X-ray Diffraction (XRD), tensile strength, Vickers hardness and bending U-shape flexure tests.

In the previous study, two Inside Temperature (IT dQ=0 and IT IM ) methods for estimating the temperature distributions in steady wave fronts in a thermoviscous material were established and the IT IM method was shown qualitatively to be effective for shock compressions where the effect of viscosity was distinguished. In this paper, these two methods are applied to the shock compressions of Yittria-doped Tetragonal Zirconia (YTZ) that is a thermoviscous material with a multiple shock Hugoniot. The YTZ Hugoniot consists of three partial curves including two kinks, that are the Hugoniot Elastic Limit (HEL) and the phase transition point. The shock temperatures evaluated by the IT IM method were close to the accurate temperatures obtained by the Walsh-Christian method in the whole stress range to 140 GPa examined here. Furthermore, the inside temperature distributions were approximately accurate because the effect of viscosity was distinguished in the shock compression. By these facts, it was considered that the fundamental assumption and the assumption on heat transport used in the IT IM method were valid and as a result, this method was effective. In addition, the influence of heat transport on the temperatures and thermoelastic stresses was examined.

This work draws attention to the to the analysis of dynamics of a nonlinear coupled cantilever beam-pendulum oscillator. Dynamical systems of this type have important technical applications, because many mechanical components consist of linear or weakly nonlinear continuos substructures such as beam coupled to nonlinear oscillators. The present paper is a continuation of the author’s previous work where in applying the Galerkin method the modal series was truncated at the first mode. In this work it is assumed that the cantilever beam behaves like an Euler-Bernoulli beam and to its end pendulum is attached. The integro-differential equations are transformed into an ordinary differential equations with the use of Galerkin procedure with beam functions. In this study, in applying the Galerkin method the modal series was truncated at the second mode. Next these equations were solved numerically and there was studied the effect of the internal friction on energy transfer in a coupled structure that consist of a linear viscoelastic beam supporting at its tip a nonlinear pendulum.

Since the middle of this century the growing fact of the unexpected environmental conditions and the rapid increase in the energy consumption have resulted in the fact that the efficient use of the energy and to exploit a new and renewable energy resources are inevitable. In the recent years, increasing importance in the issue of the best use of available energy resources are discussed with the application of the combined heat-power plants. In this paper, the performance of the conventional energy plants and combined heat-power plants are compared. For this reason a new design criterions for the combined heat-power plant are introduced here. The rationality of these new design criterions are tested in thermal energy and gas turbine plants. The obtained results are then compared with the conventional energy plants. It is proven that this new design methodology will provide more energy saving and minimize the heat losses that is produced during energy production.

A method and a measuring range of displacements and accelerations, vertical and transversal of moving parts of railway turnouts are presented in this paper. Vertical vibrations have destructive influence for railway-track construction. Transversal vibrations are in exact relation with safety of railway traffic. These vibrations are getting up from excitations of moving track vehicles. The measurements have been made in special moving turnout points. Two presently used turnouts having the same turning radius were investigated. One of them is new generation turnout, but the second one has classical construction. In finally conclusion is drawing the relation between velocity of excitation and the values of vibration parameters. Moreover explain why to use more complicated construction in turnouts of new generation.

This paper presents formulations, computations and investigations of the solutions of classes C 00 and C 11 for two dimensional viscoelastic fluid flows in u, v, p, τ ij p , τ ij s with Phan-Thien-Tanner (PTT) constitutive model using p-version least squares finite element formulation (LSFEF). The main thrust of the research work presented in the paper is to employ ‘right classes of interpolations’ and the ‘best computational strategy’ 1) to obtain numerical solutions of governing differential equations (GDEs) for increasing Deborah numbers 2) investigate the nature of the computed solutions with the aim of establishing limiting values of the flow parameters beyond which the solutions may be possible to compute, but may not be meaningful. The investigations presented in this paper reveal the following: a) The manner in which the stresses are non-dimensionalized significantly influences the performance of the iterative procedure of solving non-linear algebraic equations. b) Solutions of the class C 00 are always the wrong class of solutions of GDEs in variables u, v, p, τ ij p and τ ij s and thus spurious. c) C 11 class of solutions are the right class of solutions of the GDEs in variables u, v, p, τ ij p and τ ij s . d) In the flow domains, containing sharp gradients of the dependent variables, conservation of mass is difficult to achieve at lower p-levels (worse for coarse meshes). e) An augmented form of GDEs are proposed that always ensure conservation of mass at all p-levels regardless of the mesh and the nature of the solution gradients. f) Stick-slip problem is used as a model problem. We demonstrate that converged solutions are possible to compute for all flow rates reported and that the detailed examination of the solution characteristics reveals them to be in agreement with all the physics of the flow, g) Numerical studies with graded meshes and high p-levels presented in this paper are aimed towards establishing and demonstrating detail behavior of local as well as global nature of the computed solutions, h) Various norms are proposed and tested to judge local and global dominance of elasticity or viscous behavior i) New definitions are proposed for elongational (extensional) viscosity. The proposed definitions are more in conformity and agreement with the flow physics compared to currently used definitions j) A significant aspect and strength of our work is that we utilize straightforward p-version LSFEF with C 00 and C 11 type interpolations without linearizing GDEs and that SUPG, SUPG/DC, SUPG/DC/LS operators are neither needed nor used.

The vibration of a sandwich panel with two identical isotropic facesheets and an orthotropic core was studied. The governing partial differential equation was derived using variational principle. Kirchhoff’s theory was applied to describe the deformation of the panel, and the rotational effect was taken into consideration. The frequencies of free vibration of a rectangular panel can be predicted based on the proposed analytical model. Results based on the proposed model were compared with those from thin plate theory. The effect of orthotropic core on frequencies was also discussed.

In this paper we present and utilize a new theoretical and computational framework for computing solutions of higher classes of one dimensional transient Navier-Stokes partial differential equations in Lagrangian frame of reference using ρ, u , T variables. The approach utilizes ‘strong form’ of the governing differential equations (GDEs) and least squares method in constructing integral form. The currently used finite element approaches seek convergence of a solution in a fixed order space by h , p , or hp -adaptive processes. The fundamental point of departure in the proposed approach is that we seek the convergence of the computed converged solution over the spaces of different orders containing the basis functions. With this approach, dramatically higher convergence rates than those obtained for h , or hp -processes are achievable and the sequence of progressively converged solutions over the spaces of progressively increasing order in fact converge to the strong solution (analytical or theoretical) of the partial differential equation. It is demonstrated using one-dimensional transient Navier-Stokes equations for compressible fluid flow in Lagrangian frame of reference in ρ, u , T that in the presence of physical diffusion and dissipation, our computed converged solutions have exactly the same characteristics as the strong solutions. Compression of air in a rigid cylinder is used as the model problem.

This paper presents a new computational strategy, computational framework and mathematical framework for numerical computations of higher class solutions of differential and partial differential equations. The approach presented here utilizes ‘strong forms’ of the governing differential equations (GDE’s) and least squares approach in constructing the integral form. The conventional, or currently used, approaches seek the convergence of a solution in a fixed (order) space by h, p or hp-adaptive processes. The fundamental point of departure in the proposed approach is that we seek convergence of the computed solution by changing the orders of the spaces of the basis functions. With this approach convergence rates much higher than those from h,p–processes are achievable and the progressively computed solutions converge to the ‘strong’ i.e. ‘theoretical’ solutions of the GDE’s. Many other benefits of this approach are discussed and demonstrated. Stationary and time-dependant convection-diffusion and Burgers equations are used as model problems.

The past decade has witnessed an ever increasing interest in strengthening, repairing, retrofitting, and upgrading of deteriorated concrete structures using fiber reinforced plastics (FRP). Enhanced load carrying capacity by FRP strengthening has been observed by a large number of researchers through experiments at ambient environments. In a harsh environment, however, FRP will degrade. This may result in structural degradation of FRP strengthened concrete members. The possible structural degradation has become a major obstacle for the wide-spread acceptance of this new strengthening technique. In the present study, boiling water and ultraviolet (UV) radiation are used to study the structural degradation of concrete beams strengthened with GRFP and CFRP fabrics. A total of eighteen 170 × 7.62 × 15.2 cm steel reinforced concrete (RC) beams are prepared as control specimens, conditioned specimens, and unconditioned specimens. The test results show that environmental attacks have a considerable effect on the structural degradation of FRP strengthened concrete beams. 57% ∼ 76% of the strengthening efficiency of FRP is lost after conditioning.

The nonelastic, microscopic internal processes are generated in flowing plasma. All processes have living time different from zero. So, their influence on subsonic plasma flow can be significant. Presented paper is concerned on influence of rate collisions internal processes on subsonic flow of low temperature plasma.

The temperature distributions in overdriven steady wave fronts in 2024 Al shocked up to 80 GPa were predicted using the thermoelastic theory (Wallace theory), where the viscous stress is neglected, and the thermoviscous theory (Sano-Abe theory). The Wallace theory was improved by applying a more exact equation to the bulk modulus. As shock loading was increased, the difference between the temperature distributions predicted using each theory was greater. This tendency of the difference was similar for shocks up to 250 GPa in Pt. Thus, temperature distributions in overdriven steady wave fronts cannot be effectively evaluated using thermoelastic theory.

Two commonly used micromechanical methods, namely the method of cell and the Mori-Tanaka averaging scheme are compared in this work. Their performance is evaluated in the reference to the mechanical behavior of the composite materials. Their respective homogenization schemes are compared and evaluated through the respective strain concentration tensors that are governed by these models. The damaged elasto plastic behavior of the laminated composite system (90) (8s) and (0/90) (4s) are analyzed and compared for the two methods for the case of uniaxial loading. The Lagoudas et. a (1991) modification of the Mori-Tanaka scheme as applied to elasto-plastic constitutive models is used in this work.