Band 6, Heft 1

The buckling of rotationally restrained microbars embedded in an elastic matrix is studied within the framework of strain gradient elasticity theory. The elastic matrix is modeled in this study as Winkler’s one-parameter elastic matrix. Fourier sine series with a Fourier coefficient is used for describing the deflection of the microbar. An eigenvalue problem is obtained for buckling modes with the aid of implementing Stokes’ transformation to force boundary conditions. This mathematical model bridges the gap between rigid and the restrained boundary conditions. The influences of rotational restraints, small scale parameter and surrounding elastic matrix on the critical buckling load are discussed and compared with those available in the literature. It is concluded from analytical results that the critical buckling load of microbar is dependent upon rotational restraints, surrounding elastic matrix and the material scale parameter. Similarly, the dependencies of the critical buckling load on material scale parameter, surrounding elastic medium and rotational restraints are significant.

This work originates from an experimental program on strain distribution near the loaded surface of an airfield concrete pavement,which provided us with results that contrast with the rheological predictions of Boussinesq for a homogeneous, linear-elastic and isotropic half-space. We already reviewed and extended the original work carried out by Boussinesq in previous papers, to provide a closed form second order solution that enabled us to establish a good match between analytical and experimental findings for point-loads. In this paper, we have explained why Boussinesq’s closed form solution for a homogeneous linear-elastic and isotropic half-space subjected to a point-load is not exact, as believed until now, but approximated. Then, we have shown that our second order solution is the actual solution of Boussinesq’s problem. We have also presented the numerical analysis of second order for rectangular and elliptical contact areas, both loaded by uniform and parabolic laws of external pressure. Moreover, we have evaluated the interaction effect provided on the surface of a concrete half-space by the twin wheels of an aircraft landing gear. Extension of the solution to layered systems is also possible, for improving the knowledge of stress propagation into airfield pavements and promoting more effective design standards.

The aim of this paper is to present a further development of the Corbelling Theory [1] for assessing the structural safety of “false domes” constructions like Trulli, and more generally for corbelled domes. In particular, it is well-known that a corbelled dome of a Trullo is a layered thick shell and that only the thin inner layer (candela) has a structural role. The proposed procedure extends the capabilities of the approach proposed in [2] to more general load conditions, including the infill. The effectiveness of the proposed approach is discussed through the analysis of a paradigmatic case study of a Trullo located in Alberobello. Since the geometry of the construction plays a fundamental role in the structural behavior, the starting point of the analysis was an accurate 3D-laser scanner survey of the dome. The obtained results give some interesting insights about the role of the infill load on the equilibrium of such kind of corbelled domes.

Considerable advancements in waterjet technology take advantage of its inherent merits as a versatile machine tool have been achieved in recent years. Such advancements include, but are not limited to, process automation, machining precision, multimode machining of most materials from macro to micro scales, and cost effectiveness with fast turnaround. In particular, waterjet as a cold cutting tool does not introduce heat-affected zones (HAZ) and preserves the integrity of parent materials. As such, for heat-sensitive materials, its cutting speed is over ten times faster than those of thermal-based tools, such as solid-state lasers, electric discharge machining (EDM), and plasmas cutting. Although waterjet is basically a 2D machined tool, novel multi-axis accessories were developed to enable 3D machining and for machining on workpieces with 3D geometry. For composites, waterjet unlike mechanical routers is capable of minimizing or mitigating tearing and fraying. CNC hard tools that are in direct contact with highly abrasive composite matrix often experience rapid wearing while the heat generated by machining processes induces thermal damage to the composite. This is a nonissue for waterjet as it is a noncontact tool. The only issue for machining composites with waterjet was the damage caused by large stagnating pressure developed inside blind holes during the initial piercing operation (before breakthrough). Considerable effort was made to understand and resolve the waterjet piercing damage issue. For extremely precise parts, waterjet can serve advantageously as a near-net shaping tool; the parts can then be finished by light trimming with proper precision tools. Since the bulk of the material is removed by waterjet, the operating lives of the precision tools can be greatly extended. This paper presents a collection of waterjet-machined samples to demonstrate many benefits by applying waterjet for multimode machining of curved and layered structures.

This paper contributes an analytical nonlinear morphing model for high-amplitude corrugated thinwalled laminates of arbitrary stack-up with a corrugation shape composed of circular sections. The model describes large deformations, the nonlinear relation between line force and global stretch, and the distribution of local line loads. The quarter-unit-cell approach together with assuming small material strains and a plane strain situation contribute to the model’s simplicity. It is explained how the solution procedure minimizes the force and moment residual of the equilibrium of cutting and reaction line loads by using Newton’s optimization method. Deformation results are verified by comparison with FEM simulation. The effects of laminate design and corrugation amplitude on deformations, line-force-stretch diagrams, and bending-curvature-stretch diagrams are presented and discussed.

In this paper, two computationally efficient techniques viz. Differential Quadrature Method (DQM) and Differential Transformation Method (DTM) have been used for buckling analysis of Euler-Bernoulli nanobeam incorporation with the nonlocal theory of Eringen. Complete procedures of both the methods along with their mathematical formulations are discussed, and MATLAB codes have been developed for both the methods to handle the boundary conditions. Various classical boundary conditions such as SS, CS, and CC have been considered for investigation. A comparative study for the convergence of DQM and DTM approaches are carried out, and the obtained results are also illustrated to demonstrate the effects of the nonlocal parameter, aspect ratio (L/h) and the boundary condition on the critical buckling load parameter.

The Cell Method (CM) is an algebraic numerical method based on the use of global variables: the configuration, source and energetic global variables. The configuration variables with their topological equations, on the one hand, and the source variables with their topological equations, on the other hand, define two vector spaces that are a bialgebra and its dual algebra. The operators of these topological equations are generated by the outer product of the geometric algebra, for the primal vector space, and by the dual product of the dual algebra, for the dual vector space. The topological equations in the primal cell complex are coboundary processes on even exterior discrete p −forms, whereas the topological equations in the dual cell complex are coboundary processes on odd exterior discrete p −forms. Being expressed by coboundary processes in two different vector spaces, compatibility and equilibrium can be enforced at the same time, with compatibility enforced on the primal cell complex and equilibrium enforced on the dual cell complex. By way of example, in the present paper compatibility and equilibrium are enforced on a cantilever elastic beam with elastic inclusion. In effect, the CM shows its maximum potentialities right in domains made of several materials, as, being an algebraic approach, can treat any kind of discontinuities of the domain easily.

Forced vibration of non-uniform axially functionally graded (AFG) Timoshenko beam on elastic foundation is performed under harmonic excitation. A linear elastic foundation is considered with three different classical boundary conditions. AFG materials are an advanced class of materials that have potential for application in various engineering fields. In the present work, variation of material properties along the longitudinal axis of the beam are considered according to power-law forms. Five values of material gradation parameter provides different functional variation and their effect on the frequency response of the system is studied. The present approximate method is displacement based and Von-Karman type of geometric nonlinearity is considered with rotational component to incorporate transverse shear. Hamilton’s principle is used to derive nonlinear set of governing equation and Broyden method is implemented to solve the nonlinear equations numerically. The results are successfully validated with previously published article. Frequency vs. amplitude curve corresponding to different combinations of system parameters are presented and are capable of serving as benchmark results. A separate free vibration analysis is undertaken to include backbone curves with the frequency response curves in the non-dimensional plane.

An analytical solution is presented for the determination of deformation of curved composite beams. Each cross-section is assumed to be symmetrical and the applied loads are acted in the plane of symmetry of curved beam. In-plane deformations are considered of composite curved beams. Assumed form of the displacement field assures the fulfillment of the classical Bernoulli-Euler beam theory. The curvature of beam is constant and the internal forces in a cross-section is replaced by an equivalent forcecouple system at the origin of the cylindrical coordinate system used. The internal forces are expressed in terms of two kinematical variables, which are the radial displacement and the rotation of the cross-sections. The determination of the analytical solutions of the considered static problems are based on the fundamental solutions. Linear combination of the fundamental solutions which are filling to the given loading and boundary conditions, gives the total solution. Closed form formulae are derived for the radial displacement, cross-sectional rotation, nomral and shear forces and bending moments. The circumferential and radial normal stresses and shear stresses are obtained by the integration of equilibrium equations. Examples illustrate the developed method.

Based on the classical Kirchhoff hypothesis, the dynamic response and sound radiation of rectangular thin plates with general boundary conditions are studied. The transverse displacements of plate are represented by a double Fourier cosine series and three supplementary functions. The potential discontinuity associated with the original governing equation can be transferred to auxiliary series functions. All kinds of boundary conditions can be easily achieved by varying stiffness value of springs on each edge. The natural frequencies and vibration response of the plates are obtained by means of the Rayleigh–Ritz method. Sound radiation characteristics of the plate are derived using Rayleigh integral formula. Current method works well when handling dynamic response and sound radiation of plates with general boundary conditions. The accuracy and reliability of current method are confirmed by comparing with related literature and FEM. The non-dimensional frequency parameters of the rectangular plates with different boundary conditions and aspect ratios are presented in the paper, which may be useful for future researchers.Meanwhile, some interesting points are foundwhen analyzing acoustic radiation characteristics of plates.

This article deals with free vibration of the variable cross-section (non-uniform) single-layered graphene nano-ribbons (SLGNRs) resting on Winkler elastic foundation using the Differential Quadrature Method (DQM). Here characteristic width of the cross-section is varied exponentially along the length of the nano-ribbon while the thickness of the cross section is kept constant. Euler–Bernoulli beam theory in conjunction with Eringen nonlocal elasticity theory is considered in this study. The numerical as well as graphical results are reported by using MATLAB codes developed by authors. Convergence of present method is explored and our results are compared with known results available in literature showing excellent agreement. Further, effects various parameters on frequency parameters are studied comprehensively.

Ship collision appears as the most threatening loading accounting for structural casualties and numbers of casualties after impact on the target ship. In order to avoid such losses against collision, better safety during activities in maritime environment is demanded. Therefore, assessment of ship structure is needed to understand dynamic effect of the impact and quantify nonlinear behavior of local members. This study is conducted to achieve those aims by deploying nonlinear finite element analysis (NLFEA) to idealized ship collision event. Validation of the numerical method is performed by comparing results of a modeled collision case with various empirical calculations. Design for impact loading in main analysis considers side collision to main hull structure, which single side skin (SSS) and double side skin (DSS) types are modeled. Investigation is also directed to influence of the target members on the main hull to capacity of absorbed energy and characteristic of structural resistance. Analysis results indicate that good understanding is successfully obtained in terms of structural damage-energy relation. Confirmation of the current calculation using numerical calculation is also confirmed considering the modeled cases and empirical results agree well. Tendency of hull responses concluded that the longitudinal members contribute more to structural resistance against side collision.

In recent decades, modeling of soft fingertips has fascinated a superior momentum in research initiatives concerned with development of an anthropomorphic soft finger tip. In design and development of soft fingertips, analysis of contact a characteristic plays a vital role on dexterous manipulation. This research work presents the results of the experimental investigation in relation to the formulations of contact area for soft fingertips pressed against assorted target profiles. A dimensionless parameter, curve factor Y (r/R) is introduced to derive a parametric relationship among the key parameters. It also addresses the growth of contact area of fingertips for five different combinations. From experimental observations, a modified power law equation with conversion factor (X) is proposed to interpolate the magnitude of contact area for different profiles.

The angular deformation is key parameter in composite manufacturing for curvature surfaces. Process Induced Distortions (PID’s) are a major problem while manufacturing a composite part using autoclave process. Spring-back or spring-in is one of the PID in autoclave process. Spring-in effect either increase or decrease at angled section during curing of composite laminates. In this paper, L-shaped composite part has been manufactured using autoclave process. The material properties like glass transition temperature, heat reaction, crystallization temperature, Coefficient of Thermal Expansion have been measured for the cured component by using various testing techniques. Spring-in angle has been found for various number of layers and layup orientation. The simulation has been performed in ABAQUS software along with the COMPRO plug-in for each component. The variation of spring-in angle has been observed with changing material properties. The experimental results have been compared with simulation results. The percentage variation of spring-in deformation for experimental and simulation results has been found in the range of 5-7%.

An analytical solution is presented for the determination of the deformation of rotating two-layer composite beams. The direction of axis of rotation is vertical and the speed of rotation is constant. The axis of rotation is in the plane of symmetry of curved beam. The source of the in-plane deformation is the stationary rotation of the curved beam. The plane of the curvature is the symmetry plane of the curved beam for its material, geometrical and supporting properties. Assumed form of the displacement field meets the prescriptions of the classical Euler-Bernoulli beam theory. Examples illustrate the applications of the presented analytical solution.

In the present work, new inverse hyperbolic higher-order shear deformation theory (IHHSDT) is proposed and implemented for buckling analysis and free vibration analysis of porous Functionally Graded Material (FGM) plate on the foundation. The proposed theory follows the approximately parabolic distribution of the transverse stresses through the plate thickness and satisfies the conditions of continuity and differentiability. Three different types of porosity distribution considered. Governing differential equations (GDEs) of the plate is developed in the framework of proposed theories by Hamilton’s principle. Multiquadrics radial basis function (MQ-RBF) based Meshfree method used for discretizing the GDEs. The result obtained by the present theory is validated with the three-dimensional elastic theory and other available solutions in the literature to ensure the efficacy and accuracy of the proposed theory. Numerical results obtained for buckling and free vibration for porous FGM plate resting on the foundation. Effect of grading index, porosity fraction, porosity distribution, the effect of foundation, and the span to thickness ratio have discussed. The secured results can consider as a benchmark for future studies.

In present paper, buckling analysis is performed over laminated composite beam incorporating multi walled carbon nanotube (MWCNT) polymer matrix and then reinforced with E-glass fiber in an orthotropic manner under inplane varying thermal and mechanical loads by finite element method (FEM). Aim of the study is to develop a model which accurately perform the buckling deterministic analysis of multi-walled carbon nanotube reinforced composite laminated beam (MWCNTRCLB) with the evaluation of material property by applying Halpin–Tsai model. Combined Higher order shear deformation theory and Pasternak elastic foundation based on von Karman nonlinear kinematics and Winkler cubic nonlinearity respectively, are successfully implemented. Through minimum potential energy principle, generalized static analysis is performed using FEM, based on interactive MATLAB coding. The critical buckling load and critical buckling temperature is presented under the action of inplane variable mechanical and thermal load, with different boundary conditions, beam thickness ratio and MWCNT aspect ratio, variation with MWCNT volume fraction and coefficient of thermal expansion, with and without foundation for linear and nonlinear cases.

Analysis of concrete shallow funicular shells of rectangular plan with simply supported boundary conditions under static loads is performed using the Ritz method. Double Fourier series with the unknown constant coefficients are assumed for the displacement components of the shell and their unknown coefficients are determined such that the potential energy of the shell becomes minimum. The solution is presented in a simple form and is suitable for practical applications. The responses of rectangular–plan concrete shallow funicular shells including deflections, strains, internal forces, internal moments and stresses could be easily determined using the proposed semi-analytical method. The Ritz method results are verified against the finite element method results.

Our article is devoted to development and verification of the metaheuristic optimisation algorithm in the course of selection of the compositional proportions of the slag-filled concretes. The experimental selection of various compositions and working modes, which ensure one and the same fixed level of a basic property, is the very labour-intensive and time-consuming process. This process cannot be feasible in practice in many situations, for example, in the cases, where it is necessary to investigate composite materials with equal indicators of resistance to aggressive environments or with equal share of voids in the certain range of dimensions. There are many similar articles in the scientific literature. Therefore, it is possible to make the conclusion on the topicality of the above-described problem. In our article, we will consider development of the methodology of the automated experimental-and-statistical determination of optimal compositions of the slag-filled concretes. In order to optimise search of local extremums of the complicated functions of the multi-factor analysis, we will utilise the metaheuristic optimisation algorithm, which is based on the concept of the swarm intelligence. Motivation in respect of utilisation of the swarm intelligence algorithm is conditioned by the absence of the educational pattern, within which it is not necessary to establish a certain pattern of learning as it is necessary to do in the neural-network algorithms. In the course of performance of this investigation, we propose this algorithm, as well as procedure of its verification on the basis of the immediate experimental verification.

Shipping time, cargo handling and quality as well as operational cost are main aspects of success in trading and shipping, which leads to high demand for ship safety. During freight shipping is conducted for various cargoes, the ship structure is subjected to numbers of loads, which several of them have been predicted during ship design. Nevertheless, incidental type in form of impact load can deliver massive blow to ship safety and cause immense loss. This phenomenon may be worse than initial condition if structure of chemical-oil carrier experiences impact, which possibly evokes environmental damage to maritime territory. This work is addressed to assess crashworthiness performance of structural part, i.e. bottom tank of chemical carrier. This part is one of center point of oil spill during occurrence of the impact load. The loading conditions are defined as configuration of interaction between ship structure and rock when the ship is stranded on shallow water. A series of data observations produced by finite element analysis (FEA) provide a prediction regarding local member’s motions during the rock breaches lower parts of the bottom tank. Consequences of the plate towards failure are quantified to obtain effect of the selected impact loading conditions to directly involved (main) member and other affected local member.