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In this paper, the stress fields in nonlinear sandwich and laminated composite shells subjected to displacement-dependent loads are analyzed. To solve the problem, the geometrically exact (GeX) hybrid-mixed four-node solid-shell element is proposed. The term GeX means that the middle surface is described by analytical functions, i.e., the parametrization of the surface is known. The laminated solid-shell element formulation is based on the choice of an arbitrary number of sampling surfaces (SaS) parallel to the middle surface and located at the Chebyshev polynomial nodes within the layers, in order to introduce the displacements of these surfaces as unknown functions. The outer surfaces and interfaces are also included into a set of SaS. Due to analytical integration utilized to evaluate the tangent stiffness matrix, the developed GeX solid-shell element under non-conservative loading shows excellent performance in the case of coarse meshes and makes it possible to use only one load step in most of the considered benchmark problems. It is shown that the difference between the second Piola–Kirchhoff and Cauchy stress tensors in some non-conservative problems for sandwich and laminated shells undergoing arbitrarily large rotations can be significant. [ABSTRACT FROM AUTHOR]

This paper presents a data-driven solver (DDS) for the growth-induced deformation problems of soft materials. Contrary to the over-reliance of traditional numerical methods on material constitutive models, the DDS requires only a discrete material dataset of stress–strain pairs to describe the stress–strain relationship. With the multiplicative decomposition of the gradient tensor, the growth effects are introduced. The growth-induced deformation problems are then solved as the pre-strain problems. To overcome the difficulty in determining the growth-induced pre-stress without an explicit constitutive model, a strain-driven searching scheme is thus proposed. Several numerical examples demonstrate the robustness and its good performance of the proposed DDS. In particular, the reason for choosing the strain-driven searching scheme is also illustrated according to the numerical example results. [ABSTRACT FROM AUTHOR]

In this paper the step by step descent algorithm is extended to continuous optimization problems and applied to the optimal sizing of truss structures. The step by step descent method, recently developed, was applied to the discrete optimization of rigid structures. To solve continuous problems, a multi-stage optimization algorithm is proposed, which involves implementing the step by step descent method in multiple stages. In each stage, the continuous areas of the variables are progressively divided into a finite number of points. The algorithm is based on the search for the steepest gradient descent direction that minimizes the cost function and employs a wise heuristic approach to bypassing local optima. To evaluate the algorithm's performance, a study was carried out on ten mathematical and four truss optimization problems. For unconstrained mathematical problems, the algorithm demonstrates quick converges to optimum solution from any starting point. For truss structures, the starting design point is selected based on structural knowledge to enhance convergence speed. The obtained results surpass those achieved by other state-of-the-art optimization algorithms, affirming the efficiency, robustness and the promptness of the proposed method. [ABSTRACT FROM AUTHOR]

By gradually changing the compositions, functionally graded materials (FGMs) are constructed and possess comprehensive performance. In this paper, based on the micromechanics, the thermo-elasto-plastic behaviors of FGMs are studied with consideration of the pairwise particle interaction, where the graded microstructures of the FGMs are represented by employing a particular representative volume element (RVE). Based on the assumption that the matrix dominates the plastic behavior of the FGMs while the particles stay in their linearly elastic state, the von-Mises yield function is extended to solve FGMs problems. By employing the backward Euler's method, the overall effective thermo-elasto-plastic behavior of FGMs can be numerically obtained. When eliminating the plastic or thermal effect, the proposed model can be downgraded to the thermoelastic model or the elastoplastic model of the FGMs, respectively. In addition, the proposed model is validated with available experimental results. Finally, the effects of temperature changes, particle distributions, volume fractions, and material properties on the effective thermo-elasto-plastic properties of FGMs are studied. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of deformation of a disk rotating with changing angular velocity under consecutive accumulation of creep and plastic strains. The differential equations which help to calculate the fields of stresses, strains, displacements and velocities are obtained; the method of finite difference is used for solving the problem. The evolution of the viscoplastic flow region is investigated. The Norton power law is used as creep law; the von Mises's generalized yield criterion is applied as viscoplastic flow condition. The obtained solution is compared to the classical elastoplasticity case. A hollow disk and a disk with a rigid inclusion are studied. [ABSTRACT FROM AUTHOR]

The main purposes of the present paper are as follows: (1) to analytically derive the general solution (stress functions) for an orthotropic elastic half plane with a crack or a notch; (2) to derive the Riemann–Hilbert equation as the analytical method; (3) to solve the present problem using two methods, one is a Cauchy integral method and other is a Riemann–Hilbert method; and (4) to derive the general expressions of the stress intensity factor (SIF) for a crack problem. The stress functions obtained by the Riemann–Hilbert equation are compared with those obtained by Cauchy integral method. Then, it is confirmed that the same stress functions can be obtained. The stress functions are expressed by any elastic constants. Therefore, Mode I and II SIFs can be calculated for any elastic constants. Some examples are shown. It is stated from the results of the examples that the negative Mode I SIFs exist for certain oblique edge crack angles and elastic constants. Because the derived stress functions are expressed using a mapping function, other geometrical shapes can be analyzed by changing the mapping function. [ABSTRACT FROM AUTHOR]

In the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners. [ABSTRACT FROM AUTHOR]

Eringen's nonlocal elasticity theory is one of the most attractive approaches to investigate the intrinsic scale effect of nanoscopic structures. Eringen proposed both integral and differential nonlocal models which are equivalent to each other over unbounded continuous domains. Although the Eringen nonlocal models can be used as very useful tools for modeling the mechanical characteristics of nanoscopic structures, however, several researchers have reported some paradoxical results when they used the nonlocal differential model. In this paper, we develop a well-posed nonlocal differential model for finite domains, and its applicability to predict the static and dynamic behavior of a nanorod is investigated. It is shown that the proposed integral and differential nonlocal models are equivalent to each other over bounded continuous domains, and the corresponding elastic problems are well-posed and consistent. In addition, some paradigmatic static problems are solved the and we show that the paradoxical results disappear by using the present model. [ABSTRACT FROM AUTHOR]

This paper presents a new mathematical model for analytical investigation of global buckling behavior of slender concrete-filled steel tubular (CFST) columns with circumferential gaps and partial debonding between the concrete core and the steel tube. The analytical buckling load of circular and slender CFST columns with circumferential gaps and partial debonding is derived for the first time. The critical buckling load decreases as the magnitude and length of the circumferential gap increases. Nevertheless, it is shown that if the length of the circumferential gap is smaller than the length of the CFST column, this effect is less than 4%. On the other hand, for a fully delaminated CFST column, this effect can be up to approximately 40%. Similarly, the first buckling shape modes proved to be notably affected by the circumferential gap only if its length is greater than 75% of the CFST column length. The results can be used as a benchmark solution for the buckling problem of slender circular CFST columns with circumferential gaps and partial debonding between the materials. [ABSTRACT FROM AUTHOR]

In this paper, a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions is suggested for solving two-dimensional elastodynamic problems. The main idea is to use spherical Hankel shape functions derived from corresponding radial basis functions instead of classical Lagrange shape functions. Among the advantages of the proposed interpolation, containing the first and second kind of Bessel functions in complex space as well as the polynomial ones can be pointed out, while the classic Lagrange interpolation is only able to contain polynomial functions. The validity and accuracy of the present method are fully demonstrated using several numerical examples. For this purpose, five numerical examples are considered, and the results obtained from the proposed method (Hankel-based TD-FEM) and the Lagrange-based TD-FEM are compared with the exact analytical solutions. The results show that the use of Hankel functions in TD-FEM leads to more accurate and stable solutions rather than those obtained from the classic TD-FEM. [ABSTRACT FROM AUTHOR]

The block element method is used to study a static boundary value problem for semi-infinite lithospheric plates interacting with a deformable basement along Conrad boundary. It is assumed that the lithospheric plates have straight line boundaries parallel to each other and are considered in two positions. In the first case, the distance between the ends of the plates does not vanish, whereas in the second case the distance is absent, although the plates do not interact. It is assumed that horizontal action on the plates, which are known to move extremely slowly, is so strong that vertical components of contact stresses can be neglected. Only shift stresses remain in the contact zone. The paper addresses the comparison of numerical simulation and block element approach to investigate this problem. In the first case, appearance of a concentration of contact stresses in the zone of contact of lithospheric plates is found, while in the second case the stress concentration turns out to be singular and leads to destruction of the base or edges of the lithospheric plates. In the second case, it is possible to determine the influence of various parameters of the problem on the magnitude of the coefficients for singularities in the contact stress concentrations. The numerical method does not have this capability. The obtained result allows one to predict the starting earthquakes based on monitoring of horizontal motions of the lithospheric plates. [ABSTRACT FROM AUTHOR]

Many composite plates behave transversely isotropic. An accurate and efficient 3D analysis for the transversely isotropic plate will contribute much to the accurate design and quality promotion of this kind of structure. In this paper, a refined analysis for the transversely isotropic plate under normal loads is addressed based on the 3D Green’s function. The 3D Green’s function for the transversely isotropic plate loaded by a normal point force is derived. By adopting the general solution for the transversely isotropic material, a new harmonic function which contains undetermined constants is constructed. All stress components can be obtained by substituting the harmonic function into the general solution. The constants can be determined by considering the equilibrium and boundary conditions of the plate. For the reason that this solution satisfies the 3D governing equations rigorously everywhere in the plate, it is much more refined than that of the traditional plate theory, which is restricted by the thickness of the plate. Numerical analysis is given to discuss the efficiency and accuracy of this method and study the stress distributions in the transversely isotropic plate loaded by a normal point force and a normal distributed load, respectively. [ABSTRACT FROM AUTHOR]

In this paper, the problem of identifying the optimal amount of composite reinforcement for a given masonry structure and its optimal dislocation over the structure is addressed through the set-up of a topology optimum problem. The topological optimization theory was originally developed for searching the equilibrium path of 3D solids under sets of applied loads. The main outcome of the topology process consisted of the identification of the optimal shape of the structure resisting the given active forces. The observation of an extreme variation and a high degree of arbitrariness in selecting the refurbishment shapes in technical and experimental tests executed on masonry structures gave birth to the original idea developed by the authors of applying the topology optimization’s fundamentals to the field of FRP and FRCM refurbishment of masonry structures. The idea is essentially based on the principle that a tensile composite strip/sheet is required to work only in the areas of the masonry solid where the tensile stress cannot be avoided. If no tensile stress arises in a region of the structure, then the adoption of the reinforcement is not needed in that area since the intervention would certainly be uneconomic in this case, and it might also produce some damage to the global stability of the structure. [ABSTRACT FROM AUTHOR]

This paper deals with Noether symmetry and conserved quantities for the Hamiltonian system of Herglotz type on time scales. Firstly, the variational principle of Herglotz type for the Hamiltonian system on time scales is proposed. According to the Hamilton-Herglotz action for the Hamiltonian system on time scales and the Dubois-Reymond lemma, the Hamilton canonical equations of Herglotz type on time scales are obtained. Then, based upon the invariance of the Hamilton-Herglotz action on time scales under the infinitesimal transformations of a group, the Noether symmetric transformations for the Hamiltonian system are defined on time scales, and the criterion of the symmetry is established. Furthermore, the Noether’s theorem for the Hamiltonian system of Herglotz type on time scales is obtained because of the relationship between the Noether symmetry and conserved quantity. Besides, the Noether conserved quantities for the Hamiltonian system of Herglotz type are given in both the continuous and the discrete cases. Finally, an example is given to illustrate the application of the results. [ABSTRACT FROM AUTHOR]

In this paper, an efficient finite element (FE) solution of regular and near-regular systems is presented using graph product rules. Such systems can be observed in an FE solution of differential equations or direct construction of the stiffness matrix in a structural/mechanical problem. Graph product rules are developed to decompose a regular pattern to its preliminary generating components, solving the problem using efficient divide and conquer approaches. Regularity is regarded as a specific condition mathematically; however, due to natural repetition of elements in FE models, regular/near-regular patterns are very common in these models. In this paper, graph product mathematical formulations for FE models are developed, and the efficiency of the method is demonstrated using computational complexity. Comprehensiveness of the method is shown using diverse complementary examples. [ABSTRACT FROM AUTHOR]

In this paper, the model of a suspension bridge is composed of the main cable and beam with many discrete springs, which are used to model columns between the main cable and the deck. Based on Hamilton's variational principle, the governing equations for the in-plane dynamics of the model are obtained. The static and dynamic configuration of the beam and cable is considered in the derivation of governing equations in this paper. The boundary and continuity conditions of the subsystems (cable and beam) and the transfer matrix method are utilized to determine the only six unknown non-dimensional constants of the system. Then, the in-plane eigenvalue problem can be solved easily, and the effects of the parameters on the in-plane natural frequencies and mode shapes are systematically investigated. Finally, the results obtained by the proposed model and method are compared with those obtained by the finite element method, which shows that the proposed method applied to analyze the suspension bridge is efficient. [ABSTRACT FROM AUTHOR]

This paper uses a classical one-dimensional single-DOF model of the falling U-chain as an analytical paradigm for the assessment of a recursive modular modeling methodology, in which constraints can be enforced a posteriori. A two-dimensional nonlinear FEM model for the falling of an inextensible folded string is derived, and a numerical simulation is compared with the adopted paradigm. The proposed model not only reproduces with great accuracy the results obtained from the analytical paradigm, but also shows interesting features of this strongly nonlinear problem that might not be revealed by classical single-DOF models. [ABSTRACT FROM AUTHOR]

In this paper, some graph theoretical (topological) transformations are presented for simplifying certain problems involved in structural analysis. For each case, the main problem is stated and the proposed topological transformation is established. Once the required topological analysis is completed, a back transformation results in the solution for the main problem. The transformations studied here employ (i) models drawn on a lower dimensional space, (ii) models embedded on higher dimensional spaces and (iii) interchange models which have simpler connectivity properties than the corresponding original structural models. All these transformations are illustrated utilizing simple examples. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to provide an efficient method for finding steady planar ideal plastic flows of anisotropic materials. The method consists of determining two mappings between coordinate systems. One of these mappings is between principal lines-based and characteristics-based coordinate systems, and the other is between Cartesian- and characteristics-based coordinate systems. Thus, the mapping between the Cartesian- and principal lines-based coordinate systems is given in parametric form. It is shown that the boundary value problem of finding the mapping between the principal lines-based and characteristics-based coordinate systems can be reduced to the solution of a telegraph equation where two families of characteristics are curved and to the evaluation of ordinary integrals where one family of characteristics is straight. In either case, after solving this problem the problem of finding the mapping between the Cartesian- and characteristics- based coordinate systems can be reduced to the evaluation of ordinary integrals. [ABSTRACT FROM AUTHOR]

In this paper a new graph-based evolutionary algorithm, gM-PAES, is proposed in order to solve the complex problem of truss layout multi-objective optimization. In this algorithm a graph-based genotype is employed as a modified version of Memetic Pareto Archive Evolution Strategy (M-PAES), a well-known hybrid multi-objective optimization algorithm, and consequently, new graph-based crossover and mutation operators perform as the solution generation tools in this algorithm. The genetic operators are designed in a way that helps the multi-objective optimizer to cover all parts of the true Pareto front in this specific problem. In the optimization process of the proposed algorithm, the local search part of gM-PAES is controlled adaptively in order to reduce the required computational effort and enhance its performance. In the last part of the paper, four numeric examples are presented to demonstrate the performance of the proposed algorithm. Results show that the proposed algorithm has great ability in producing a set of solutions which cover all parts of the true Pareto front. [ABSTRACT FROM AUTHOR]

This paper studies the periodic notch problem with arbitrary configuration. A complex variable boundary integral equation (CVBIE) is suggested to solve the problem. The periodic notch problem is considered as a superposition of infinite single notch problems. The influence on the domain point from the assumed boundary traction on the notch contour is reduced to formulate a matrix. In this paper, this matrix is formulated completely after the relevant BIE is solved in a matrix representation. The remainder estimation technique is suggested to evaluate the influence to the central notch from many (form N-th to infinity) neighboring notches. Many computed results for the stress concentration factor for the elliptic and square notches are carried out. The stacking effect is also studied. [ABSTRACT FROM AUTHOR]

It is well known that the main approaches of the analytical solving of the elasticity mixed plane problems for a semi-strip are based on the different representations of the equilibrium equations' solutions: the representations through the harmonic and by harmonic functions, through the stress function, Fadle-Papkovich functions and so on. The main shortcoming of these approaches is connected with the fact that to obtain the expression for the real mechanical characteristics, one should execute additional operations, not always simple ones. The approach that is proposed in this paper allows the direct solution of the equilibrium equations. With the help of the matrix integral transformation method applied directly to the equilibrium equations, the initial boundary problem is reduced to a vector boundary problem in the transformation's domain. The use of matrix differential calculations and Green's matrix function leads to the exact vector solution of the problem. Green's matrix function is constructed in the form of a bilinear representation which simplifies the calculations. The method is demonstrated by the solving of the thermoelastic problem for the semi-strip. The zones and conditions of the strain stress occurrence on the semi-strip's lateral sides, important to engineering applications, are investigated. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to address the wave reflection and refraction in the rotating piezoelectric crystals subjected to a biaxial, homogeneous stress field. Besides, utilizing the inhomogeneous wave theory enables additional reflected and refracted surface waves to solve the problem of discrepancy between independent wave modes and boundary equations. A set of homogeneous equations in displacements and electric potential is derived within the rotatory coordinate system in the presence of the Coriolis and centrifugal acceleration. The performed plane example shows that there is a critical point when angular velocity equals the wave frequency, at which no quasi-longitudinal wave can be generated, reflected or refracted, and close to which the characteristics of the quasi-longitudinal wave change sharply. In addition, the presence of the Coriolis and centrifugal accelerations demonstrates noticeable influence upon the wave propagation and reflection/refraction, namely the wave velocities and attenuations, the angles of the reflected/refracted bulk waves, the reflection/refraction amplitudes and energy ratio coefficients. The analysis results also indicate that the reflected and refracted waves can transform into the type of surface wave at some incident angles. Finally, compared with the rotation effects, the waves are not sensitive to the initial stresses. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a solution for the coupled flexure-torsion De Saint Venant problem for orthotropic beams taking full advantage of the complex variable boundary element method (CVBEM) properly extended using a complex potential function whose real and imaginary parts are related to the shear stress components, the orthotropic ratio and the Poisson coefficients. The proposed method returns the complete stress field and the unitary twist rotation of the cross section at once by performing only line integrals. Numerical applications have been reported to show the validity and the efficiency of the proposed modified CVBEM to handle shear stress problems in the presence of orthotropic materials. [ABSTRACT FROM AUTHOR]

This paper presents a semi-analytic solution for multiple cracks beneath a half-space surface under elastohydrodynamic lubrication (EHL) contact. The solution not only takes into account the fluid-structure interactions in the EHL contact but also the interactions among all the cracks. In developing the governing equation, each crack of mixed modes I and II is modeled as a continuous distribution of climb and glide dislocations with unknown densities. With such a treatment, the original problem for materials with multiple cracks is converted into two subproblems: a homogeneous EHL contact problem with the fluid pressure distribution and the lubricant film thickness to be determined, and a half-space problem with unknown dislocation densities, which are iteratively obtained by a modified conjugate gradient method. A numerical algorithm is developed to integrate the two problems. The computational process is performed until the convergence of the displacements, which are the sum of the displacements due to the fluid pressure and the subsurface cracks. Sample cases are presented to analyze the pressure and lubricant film thickness profiles of EHL contact and the subsurface stresses for cracked materials. [ABSTRACT FROM AUTHOR]

This paper is concerned with the theoretical treatment of transient thermoelastic problems involving a multilayered hollow cylinder with piecewise power law nonhomogeneity due to the asymmetrical heating of its surfaces. The thermal and thermoelastic constants of each layer are expressed as power functions of the radial coordinate, and their values continue on the interfaces. The exact solution for the two-dimensional temperature change in a transient state is obtained using the Laplace transformation and separation-of-variables method. The exact solution for the thermoelastic response of a multilayered hollow cylinder under the state of generalized plane strain, where the strain is not bound, is obtained herein. Some numerical results for the temperature change and the stress distributions are presented in figures. The influence of the functional grading on the thermal stresses is investigated. Furthermore, the influence on the axial stress of the restraint condition in the axial direction is investigated. [ABSTRACT FROM AUTHOR]

This paper proposes an improvement of the Legendre polynomial series method to solve the harmonic wave propagation in multilayered piezoelectric spherical plates, which are used in point-focusing transducers. The conventional Legendre polynomial method can deal with the multilayered structures only when the material properties of two adjacent layers do not change significantly and cannot obtain correctly normal stress and normal electric displacement shapes unlike the proposed improved orthogonal polynomial approach which overcomes these drawbacks. Detailed formulations are given to highlight its differences from the conventional Legendre polynomial approach. Through the comparisons of numerical results given by an exact solution (obtained from the reverberation-ray matrix method), and by the conventional polynomial approach and the improved polynomial approach, the validity of the proposed approach is illustrated. The influences of the radius-to-thickness ratio on dispersion curves, stress and electric displacement distributions are discussed. It is found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: radius-to-thickness ratio, wave speed, and position of the component material. [ABSTRACT FROM AUTHOR]

In this paper, a new semi-analytical method is developed for solving two-dimensional elastodynamic problems in the frequency domain, employing Fast Fourier Transform. Using specific non-isoparametric elements, the boundary of the problem's domain is discretized. By employing higher-order Chebyshev mapping functions, special shape functions, Clenshaw-Curtis quadrature, and implementing a weak form of weighted residual method, coefficient matrices of equation system become diagonal. This fact results in a set of decoupled Bessel differential equations to be used for solving the whole system. This means that the governing Bessel differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. For each DOF, the Bessel differential equation is solved for a specific frequency. Finally, the time history of responses may be obtained by using Inverse Fast Fourier Transform. Three numerical examples are presented to demonstrate the accuracy of the present new method. [ABSTRACT FROM AUTHOR]

The dynamic behavior of friction-induced vibration problems is governed by second-order differential equations having asymmetric matrices, due to the coupling of structures and external loads, which are functions of some parameters. Asymmetric systems are prone to unstable vibration (flutter) as a parameter reaches a critical value. Placement of these unstable poles to the left-hand half of the complex pole plane for stabilization can be achieved by active (feedback control) and passive means (structural modification). Moreover, placement of poles is also done to achieve the desirable dynamic response and system performance. However, such active pole assignment control introduces inherent time delays in the feedback control loop. This paper presents a method for assigning complex poles to second-order damped asymmetric systems by using state-feedback control while considering a constant time-delay in the feedback control loop. The control strategy is based on receptances of the symmetric part of the asymmetric open-loop system (without time delay), which can be easily obtained from transfer function measurements. This method does not require the knowledge of mass, damping and stiffness matrices, and hence circumvents the modeling errors (finite element or reduced order). In this research, with numerical examples, it is shown that by means of active state feedback control and by using a relatively small number of available receptances, open-loop poles of the asymmetric system can be assigned precisely. The stability of the closed-loop system is analyzed by computing primary closed-loop poles and the associated critical time delay. [ABSTRACT FROM AUTHOR]

It has been shown recently that the class of elastic bodies is much larger than the classical Cauchy and Green elastic bodies, if by an elastic body one means a body incapable of dissipation (converting working into heat). In this paper, we study the boundary value problem of a hole in a finite nonlinear elastic plate that belongs to a subset of this class of the generalization of elastic bodies, subject to a uniaxial state of traction at the boundary (see Fig. 1). We consider several different specific models, including one that exhibits limiting strain. As the plate is finite, we have to solve the problem numerically, and we use the finite element method to solve the problem. In marked contrast to the results for the classical linearized elastic body, we find that the strains grow far slower than the stress. [ABSTRACT FROM AUTHOR]

In this paper, the constitutive relations of the finite element method are constructed and used for solving two- and three-dimensional problems of the asymmetric theory of elasticity. Different variants of finite elements are considered. The numerical experiments are carried out to evaluate the reliability and computational efficiency of the finite element algorithm based on the comparison between the numerical and analytical solutions, numerical estimation of the convergence and checking of the degree of accuracy, to which the natural boundary conditions are satisfied. The obtained solutions to the two- and three-dimensional problems are interpreted from the viewpoint of their applicability to a design of experiments capable of revealing the facts of couple-stress effects in material under elastic deformation and identification of material constants for the asymmetric theory of elasticity. The capabilities of the finite element algorithm to interpret experimental data and estimate the errors occurring in real experiments have been tested by solving several example problems. [ABSTRACT FROM AUTHOR]

In this paper, the following new results related to Rayleigh waves in incompressible elastic media under the influence of gravity are presented: (i) the exact formulas for the velocity of Rayleigh waves propagating along the free-surface of an incompressible isotropic elastic half-space under the gravity are derived, and (ii) two approximate formulas for the velocity of the Rayleigh waves are established and it is shown that their accuracy is very high. To derive the exact formulas, we use the theory of cubic equation, and to establish the approximate formulas, we employ the best approximate second-order polynomials of the cubic power. The obtained formulas are powerful tools for analyzing the effect of gravity on the propagation of Rayleigh waves and for solving the inverse problem. [ABSTRACT FROM AUTHOR]

A unified generalized thermoelasticity solution for the transient thermal shock problem in the context of three different generalized theories of the coupled thermoelasticity, namely: the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation is proposed in this paper. First, a unified form of the governing equations is presented by introducing the unifier parameters. Second, the unified equations are derived for the thermoelastic problem of the isotropic and homogeneous materials subjected to a transient thermal shock. The Laplace transform and inverse transform are used to solve these equations, and the unified analytical solutions in the transform domain and the short-time approximated solutions in the time domain of displacement, temperature and stresses are obtained. Finally, the numerical results for copper material are displayed in graphical forms to compare the characteristic features of the above three generalized theories for dealing with the transient thermal shock problem. [ABSTRACT FROM AUTHOR]

In recent years, the importance of economical considerations in the field of structures has motivated many researchers to propose new methods for minimizing the initial and life cycle cost of the structures subjected to seismic loading. In this paper, a new framework is presented to solve the performance-based multi-objective optimization problem considering the initial and life cycle cost of large structures. In order to solve this problem, a non-dominated sorting genetic algorithm (NSGA-II) using differential evolution operators is employed to solve the optimization problem, while a specific meta-model is utilized for reducing the number of fitness function evaluations. The required computational time for pushover analysis is decreased by a simple numerical method. The constraints of the optimization problem are based on the FEMA codes. The presented results for application of the proposed framework demonstrate its capability in solving the present complex multi-objective optimization problem. [ABSTRACT FROM AUTHOR]

A new statement for a certain contact problem subclass is proposed. The statement is based solely on a weak solution notion for the equilibrium equation and does not utilize both optimization theory (penalty, Lagrangian multipliers and augmented Lagrangian) and mathematical programming. An inverse theorem is proved. Numerical examples for the 2-D case are given. The approach reported in this paper allows to define the law for movement of the rigid body, which acts on the deformable one with the force changeable in compliance with the prescribed program. This is the primary distinction from other works devoted to the contact subjects, and is very important for practical applications where the rigid body is the deforming tool. [ABSTRACT FROM AUTHOR]

In this paper, we investigate free thickness-shear and thickness-twist vibrations of a finite crystal resonator of AT-cut quartz carrying a thin mass layer at the central portion of its top surface operating as a quartz crystal microbalance. The equations of anisotropic elasticity are used with the omission of the small elastic constant c. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes and vibration confinement by the mass layer are calculated and examined. [ABSTRACT FROM AUTHOR]

In the proposed paper, a new problem on the steady-state oscillations of an elastic infinite cone is solved for the point oscillating force enclosed to a cone's vertex. On a cone's conic surface, the stresses are given. The auxiliary problem for a cone truncated by a spherical surface is formulated with the aim to obtain the solution of the initial problem. The solution is constructed with the help of the integral transformation method and the method of Green's function. The limiting transition in the solution's formulas is carried out to obtain the exact solution of the initial problem. The calculation of the displacements and the stress wave field of the cone is performed. [ABSTRACT FROM AUTHOR]