Thin-walled Structural Elements Research Articles

Determination of the Period of Subcritical Growth of Creep-Fatigue Cracks Under Block Loading

We formulate a mathematical model for the investigation of the processes of propagation of creepfatigue cracks in plates under block loading. The influence of the shape of loading blocks on the durability of structural elements is investigated and the the subcritical growth of creep-fatigue cracks in thin-walled structural elements is analyzed.

Practical Stability of the “Cross” Scheme in the Numerical Integration of Dynamic Equations for Flexible Thin-Walled Structural Elements Obeying the Hypotheses of the Timoshenko Theory

In the von Karman approximation, we formulate the initial boundary-value problem of the dynamics of flexible isotropic and composite elastic beams-walls within the framework of two versions of the Timoshenko theory. We perform a qualitative analysis of the resolving system of equations of motion. It is shown that, in the geometrically linear statement, the dynamics of elastic beams is described by a hyperbolic system. At the same time, in the case of deformation of flexible beams, the system of resolving motion equations may change its type degenerating from a hyperbolic system into a system of mixed (composite) type. We develop finite-difference and variation-difference versions of the explicit (in time) “cross” scheme for the numerical integration of the posed initial boundary-value problems. On the basis of these numerical methods, we perform the numerical analyses of the dynamic flexural deformation of flexible metallic and composite beams under explosive-type loads. The result of these calculations demonstrate that, in almost cases, one can indicate the levels of loading of flexible beams under which the “cross” scheme becomes unstable, although the condition of stability obtained in the linear approximation is satisfied with a considerable margin. Thus, it is shown that, in the case of dynamic analysis of flexible beams, one can speak only about the practical stability of the “cross” scheme but not about its conditional stability.

Параметризация элементов конструкций сложной геометрии

Experimental approach of parametrization of three-dimensional bodies and thin-walled elements of structures of complex geometry is considered Algorithm for constructing a spa- tial network, as well as determining the coordinates, components of the metric tensor and Christoffel symbols are given. Efficiency of modeling elements of complex geometry by a spline version of the finite element method is discussed

Method of increasing durability of thin-walled structural elements

The article analyzes how efficient damping introduced into designs of structural elements by means of such light fillers as foam plastics could be. It cites the results of computing experiments designed to assess how the number of significant free vibration cycles depends on the width of a beam wall and the height of a filler layer. The prediction is made of a substantial increase in durability of the machines which operate in a dynamic impulse-loading mode.

Study of stress-deformed state of rectangular plates based on nonclassical theory

The construction of a three-dimensional theory of rectangular plates free of the Kirchhoff–Love hypotheses has been considered. The asymptotic integration of differential equations of three-dimensional problem of the elasticity theory has been used to clarify the results of classical theory in narrow boundary zones of the plate. This article has been focused on identifying the stress-deformed state (SDS) of the boundary layer type near rigidly and elastically fixed edges by the plate where the destruction of thin-walled structural elements in machinery, including aviation and space technology, takes place.

Anomalous Refraction of Acoustic Guided Waves in Solids with Geometrically Tapered Metasurfaces.

The concept of a metasurface opens new exciting directions to engineer the refraction properties in both optical and acoustic media. Metasurfaces are typically designed by assembling arrays of subwavelength anisotropic scatterers able to mold incoming wave fronts in rather unconventional ways. The concept of a metasurface was pioneered in photonics and later extended to acoustics while its application to the propagation of elastic waves in solids is still relatively unexplored. We investigate the design of acoustic metasurfaces to control elastic guided waves in thin-walled structural elements. These engineered discontinuities enable the anomalous refraction of guided wave modes according to the generalized Snell's law. The metasurfaces are made out of locally resonant toruslike tapers enabling an accurate phase shift of the incoming wave, which ultimately affects the refraction properties. We show that anomalous refraction can be achieved on transmitted antisymmetric modes (A_{0}) either when using a symmetric (S_{0}) or antisymmetric (A_{0}) incident wave, the former clearly involving mode conversion. The same metasurface design also allows achieving structure embedded planar focal lenses and phase masks for nonparaxial propagation.

Identification of the geometry and elastic properties of rigid inclusions in thin plate

The presence of inclusions in thin-walled structural elements in the course of their operation under mechanical and thermal loads gives rise to the material damage. In publications on this subject, the problem of defect identification is considered in two directions – the location and shape of the defect or the physical properties of rigid inclusions are determined. The paper proposes a method for simultaneous determination of the location of rigid inclusions and their elastic properties (Young's modulus) in a thin plate. The mathematical model of a plate with the inclusion is built in the framework of the linear theory of elasticity. For quantization of unknown functions, the finite element method is used. The geometric inverse problem is formulated in the conditional-correct statement. The parameters of rigid inclusions are determined by minimizing the quality functional. Additional conditions are attached to the functional using the Lagrange multipliers. The results of the identification of one or several inclusions of different sizes by the proposed method are presented. In solving the problem for a plate with one rigid inclusion, the error of restoration of the inclusion location does not exceed 3 %, the error of determination of the Young's modulus of this inclusion – 2 %. The error of determination of the Young's modulus for a group of several rigid inclusions is in the range of 4–7 %. Comparative analysis of numerical experiment results shows that the proposed method allows identifying the location and properties of several rigid inclusions of various sizes. Solution of the problem of identifying the inclusions, determining their size and elastic properties allows more accurate estimation of the strength characteristics of elements and prediction of the service life of structures.

Smart textile reinforcement with embedded stainless steel yarns for the detection of wetting and infiltration in TRC structures

This study examines the feasibility of smart textile reinforced concrete (TRC) elements with self-sensing capabilities that are based on stainless steel yarns knitted in the textile grid. The self-sensory structural element combines the advantages of the glass fiber based TRC technology for thin-walled structural elements with those stemming from the electrical properties of yarns made of stainless steel filaments knitted in the textile fabric. The current study explores the ability of the yarns to sense humidity governed by infiltration of water through cracked zones along the structure. To examine this concept and its potential feasibility, a TRC beam specimen with stainless steel sensory yarns knitted in a glass fiber fabric is tested and monitored under different environmental conditions. The paper looks into the ability of the embedded steel yarns to detect wetting through the comparison of four electrical schemes and four sensing concepts. The results of the tests demonstrate the features of each sensory scheme and reveal its potential use as a basis for functional monitoring in TRC structures.

Large Deflections of Elastic Rectangular Plates

It is known that elastic large deflections of thin plates are governed by von Karman nonlinear equations. The analytical solution of these equations in the general case is unfeasible. Samuel Levy, in 1942, showed that large deflections of the rectangular plate can be expressed as a double series of sine-shaped harmonics (deflection harmonics). However, this method gave no way of creating the computer algorithm of solving the problem. The stress function expression taken in the Levy's method must be revised to find the approach that takes into account of all possible products of deflection coefficients. The algorithm of solving the problem for the rectangular plate with an arbitrary aspect ratio under the action of the lateral distributed load is reported in this paper. The approximation of the plate deflection is taken in the form of double series proposed by Samuel Levy. However, the expression for the stress function is presented in the form that incorporates products of deflection coefficients in the explicit form in distinction to the Levy's expression. The number of harmonics in the deflection expression may be arbitrary. The algorithm provides composing the system of governing cubic equations, which includes the deflection coefficients in the explicit form. Solving the equation system is based on using the principle of minimum potential energy. A method of the gradient descent is applied to find the equilibrium state of the plate as the minimum point of the potential energy. A computer program is developed on the basis of the present algorithm. Numerical examples carried out for the plate model with 16 deflection harmonics illustrate the potentialities of the program. The results of solving the examples are presented in the graphical form for the plates with a different aspect ratio and may be used under designing thin-walled elements of airplane and ship structures.

Acoustic meta-structures based on periodic acoustic black holes

This paper presents a class of three-dimensional fully isotropic acoustic metamaterials that support the development of load-bearing thin-walled structural elements with engineered wave propagation characteristics, i.e. the meta-structures. This class of metamaterials is based on the concept of Acoustic Black Hole (ABH) that is an element able to bend and, eventually, trap acoustic waves. A periodic lattice of ABHs enables wave propagation characteristics comparable with resonant metamaterials but without the need and the fabrication complexity associated with the use of either multi-material or locally resonant inclusions. The dispersion characteristics show the existence of several interesting phenomena such as strong mode coupling, zero group velocity points on the fundamental modes, and Dirac points at the center of the Brillouin zone. Numerical simulations, conducted on a meta-structure made of a thin metal plate with an embedded slab of ABH material, show the existence of a variety of wave propagation effects (e.g., collimation and bi-refraction) in an extended operating range. Such an engineered material can pave the way to the design of thin-walled adaptive structures with fully passive wave management capabilities.

Parametric Vibration of Multilayer Plates of Complex Shape

UDC 539.3 aa numerical-analytic method for the investigation of parametric vibrations of the plates under the action of static and periodic loads applied in the middle plane. The method is used for the equations of motion of plates obtained within the framework of the classical theory. The developed approach is based on the application of the theory of R -functions and variational methods, which enables us to study plates of arbitrary geometric shapes with various boundary conditions. According to the proposed approach, we first find the subcritical state of the plate if it is not homogeneous. To construct the zones of dynamic instability, we use the method proposed by Bolotin. The results obtained with the help of the developed approach are compared with the available data. We solve a number of new problems for multilayer plates of complex geometric shapes with holes. The investigation of parametric vibration of multilayer composite plates is an important urgent problem of the contemporary nonlinear mechanics. As a specific feature of this class of problems, we can mention possible loss of stability for certain values of the parameters of loading, which leads to undesired consequences and even to the fracture of structures. In view of the fact that actual elements of thin-walled structures usually have holes, notches, and, generally speaking, arbitrary geometric shapes, which substantially affects the subcritical state of the plate, it is necessary to develop universal algorithms capable of determination of the subcritical state. For the state-of-the-art of this problem, the reader is referred to the works by Sahu and Datta [10], Dash, Asha, and Sahu [7], Simitses [11], Ng, Lam, and Reddy [9], Nemeth [8], etc. By analyzing the cited works, one can make a conclusion that numerical-analytic approaches to the investigation of parametric vibrations of multilayer plates of complex geometric shapes and in the case of inhomogeneity of the plates are practically absent. A method proposed in the present work can be regarded as a universal approach that enables one to take into account the subcritical state and investigate multilayer plates with complex shape in the plan. For one-layer isotropic and orthotropic plates, a similar approach based on the R -function theory and variational methods (RFM) [5] was developed in [6]. The novelty of the present work is connected with the development of the RFM for the investigation of stability of multilayer plates of symmetric structure. In this case, we write (in the analytic form) the expressions for the coefficients of the system of ordinary differential equations obtained by reduction of the original system of motion with the help of multimode approximation of the unknown functions.

Evaluation of the Influence of the Diameter and Shape of Lightening Holes on Effort of Webs and Values of Critical Forces of Thin-Walled Girders

This article is dedicated to analysis of the impact of lightening holes (performed in the webs of girders, ribs, etc. elements of thin-walled structures) on the value of the critical forces and local effort of the material webs girders. Paper presents the results of typical analysis of two flanges thin-walled girders. Calculations was performed for one of the three most common ways of making lightening holes which differ in the way the edge of the hole shaping. Analysis includes the most common case of work of this construction type - that is the case in which the load acts in the plane of web girder. The article presents a comparison of the results of girders with holes with the results for the full girders (without holes). Particular attention was paid to the significant increase the stress concentration caused by the occurrence of holes.

Translation of W. Wunderlich’s “On a Developable Möbius Band”

The following is a translation of Walter Wunderlich’s article “Uber ein abwickelbares Mobiusband”, which appeared in the Monatshefte fur Mathematik66 (1962), 276–289 and was dedicated to Prof. Dr. Paul Funk on the occasion of his 75th birthday. Wunderlich summarizes Sadowsky’s work (Sitzber. Preuss. Akad. Wiss. 22:412–415, 1930; Verhandlungen des 3. Internationalen Kongresses fur Technische Mechanik, II (Stockholm, 1930), pp. 444–451, Sveriges Litografiska Tryckerier, Stockholm, 1931) on developable Mobius bands and improves Sadowsky’s upper bound of the dimensionally-reduced variational description for determining the configuration of a Mobius band whose width is small in comparison to its length. Attempting to reproduce the equilibrium depiction of a band of finite width, using a rational-algebraic developable, Wunderlich then extends Sadowsky’s results by presenting perhaps the first successful model of a closed, analytic, developable Mobius band with associated thinness bounds. This translation makes Wunderlich’s work accessible to the broader research community at a time of growing interest in and relevance of thin-walled structural elements.

Theoretical Principles of Determining the Longitudinal Thermal Conductivity of Thin-Walled Structural Elements from Composite Materials

We propose a method for determining the longitudinal thermal conductivity of thin-walled structural elements from composite materials involving the formation in the sample of the investigated material of a nonstationary temperature field whose gradient coincides with the direction of the reinforcement plane. We have made estimates of the influence of the main methodological errors of the proposed method on the determination accuracy of the thermal conductivity of the material.

Simulation of the steady-state creep of crossreinforced metal composites with account of anisotropy of phase materials 2. The case of 2D reinforcement

Iterative models are proposed to describe the mechanical behavior of thin-walled metal-composite structural elements, cross-reinforced in a plane, whose incompressible phase materials operate under the conditions of steady-state anisotropic creep. A comparative analysis of the calculations performed is carried out for different structural models of the mechanical behavior of annular metal-composite plates under the conditions of steadystate creep.

Possibility of using Nd:YAG laser for precise joining of thin-walled elements of structures on the example of the flow sensor pitot probe

The expansion of laser technology applications is more intense, with higher requirements for welded structures, and higher the performance demanded in the joining technology industry. Laser technol...

Mathematical modeling of fatigue fracture of plates with cracks under block loading

A mathematical model for studying the fatigue fracture of thin-walled structural elements (plates) with cracks under block loading is formulated. The influence of the form and structure of loading blocks on the residual lifetime of a plate is investigated.

Improved mechanical properties of textile reinforced concrete thin plate

Textile reinforced concrete (TRC) is especially suitable for the thin-walled and light-weight structural elements with a high load-bearing capacity. For this thin element, the concrete cover thickness is an important factor in affecting the mechanical and anti-crack performance. Therefore, the influences of the surface treatment of the textile and mixing polypropylene fiber into the concrete on the properties of the components with different cover thickness were experimentally studied with four-point bending tests. The experimental results show that for the components with the same cover thickness, sticking sand on epoxy resin-impregnated textile and adding short fiber into the concrete are helpful to improve their mechanical performance. The 2–3 mm cover thickness is enough to meet the anchorage requirements of the reinforcement fiber and the component has good crack pattern and mechanical behavior at this condition. Comparison between the calculated and the experimental values of flexural capacity reveals satisfactory agreement. Finally, based on the calculation model of the crack spacing of reinforced concrete structures, the crack extension of this thin-wall component was qualitatively analyzed and the same results with the experimental were obtained.

Experimental Detection of Functional Properties of the Semi-Rigid Fillers

Possibility of quick fixes or need to extend life of existing thin-walled structural elements, such as pressure vessels, piping and other, workers under internal pressure media, seems promising application of pressurized protecting sleeve. Such a sleeve could consist of a divided metal housing or jacketed sleeve and curable sealing elements or curable filling materials. This solution is particularly suitable for repairing corrosion-damaged pipelines. The main problem of this technology is to select an existing filling material. Materials as fillers must meet a number of specific requirements. One of the main goals was to determine the rate of decline in the relative volume changes and the rate of pressure drop. Appropriate method was chosen using the results of strain measurement.

Long-term strength of thin-walled structural elements with low-temperature creep cracks

We formulate a criterion for the evaluation of the long-term strength of structural elements with low-temperature creep cracks under long-term static loading. The application of the proposed criterion is illustrated by an example of problems posed for beams of open profile containing cracks subjected to long-term tension and bending.