Smart control of cylindrical shells incorporating Murakami Zig-Zag function

p-Version axisymmetric shell element for geometrically nonlinear analysis

• Deriving equilibrium equations for cylindrical shells with viscoelastic functionally graded properties (VFG). • Viscoelastic properties are modeled using Zener three-parameter models for shear behavior, while assuming elastic behavior for bulk properties. • The loadings consist of axial and lateral pressures, either long or short duration, and continuous or piecewise distribution. The presented solution does not depend on the duration of loading. • No need for new modeling for sensitivity analysis and optimization. This manuscript presents an analytical method for determining the deformations of cylindrical shells with viscoelastic functionally graded (VFG) properties under axial and transverse pressures. The displacement field follows first-order shear deformation theory (FSDT), with a standard linear solid (SLS) model representing viscoelastic behavior. Property variations through the shell thickness are modeled using a continuous power function. Kinematics adhere to von Kármán relations, and Hooke's law serves as the constitutive equation. Equilibrium equations are derived via the virtual work principle, resulting in a system of coupled nonlinear partial differential equations. The Galerkin method is applied to remove the spatial part of the equations. The remaining ordinary differential equations are solved analytically using the multiple-scale method. The results indicate the creep phenomenon of the shell under constant loads. Sensitivity analysis shows that the power law index as well as the viscoelastic properties can affect the deformation rate. Additionally, for piecewise loading, recovery behavior is observed in the response. The analytical procedure presented can be an effective formulation for optimization through trial and error. The results are compared with the finite element (FE) method for special cases.

The paper presents a comparison between two existing zigzag functions that are used to improve equivalent single layer (ESL) theories for the analysis of multilayered composite and sandwich beams. ESL theories are easy to implement and computationally affordable but, in order to correctly describe the mechanical behavior of laminated structures (especially those exhibiting high transverse anisotropy or high thickness-to-side length ratios), the displacement field needs to be enriched by a through-the-thickness piecewise linear contribution denoted as “zigzag.” The zigzag term of the displacement field is used to model the local distortion of the cross section in each lamina of multilayered structures and is related to the continuity of transverse stresses. The paper considers two zigzag functions that have been proposed in the open literature (namely Murakami's zigzag function and the refined zigzag function) and compares their performances when they are used to improve the classical Timoshenko beam theory; both displacement-based and mixed formulations are considered. To the best of the author's knowledge, such a comparative study has never been published. The problem of a simply supported beam subjected to a transverse distributed load is considered as a test case. Several stacking sequences, ranging from monolithic to sandwich-like and from symmetric to arbitrary, are considered. The special case of laminates with external weak layers is also investigated and the effects of these lay-ups on the derivation of the refined zigzag function are analyzed for the first time. The capability of the tested zigzag functions to help evaluate the overall deflection and model the through-the-thickness distribution of the axial displacement and stress is investigated. It has been recognized that the refined zigzag function is more accurate, especially for unsymmetric and arbitrary lay-ups and can be adopted to efficiently introduce zigzag kinematics into any ESL theory.

Nonlinear flutter of aerothermally buckled composite shells with damping treatments

In the present study, the static analysis of functionally graded material (FGM) double-curvature shells, using a quasi-3D fifth-order shear and normal deformation theory, is presented. The aim is to study the structural response of the FGM porous sandwich plates and shells by employing the higher-order shear and normal deformation theory, with a fifth-order polynomial in the displacement field. The analysis predicts the deflection and stresses and shows the porosity effects on the bending behavior of FGM porous shells. The governing equations are derived using the principle of virtual work done, and the Navier solution scheme is then utilized to solve them. MATLAB coding is used to obtain the numerical results using the present theory. The numerical result includes the deflection and stresses in cylindrical, spherical, hyperbolic, and elliptical shells under sinusoidal and uniformly distributed load. The current study’s findings are validated by contrasting them with those in the literature and observing that the displacements and stresses increase with the power-law index, which is consistent with the expected behavior of FGM shells under loading. A few other findings for the static analysis of plates and shells are also obtained, which may be helpful for future studies in the field.

Electrical stimulation devices can be used as adjunct therapy to lumbar spinal fusion to promote bone healing, but their adoption has been hindered by the large battery packs necessary to provide power. Piezoelectric composite materials within a spinal interbody cage to produce power in response to physiological lumbar loads have recently been investigated. A piezoelectric macro-fiber composite spinal interbody generated sufficient power to stimulate bone growth in a pilot ovine study, despite fabrication challenges. The objective of the present study was to electromechanically evaluate three new piezoelectric disc composites, 15-disc insert, seven-disc insert, and seven-disc Compliant Layer Adaptive Composite Stack (CLACS) insert, within a spinal interbody, and validate their use for electrical stimulation and promoting bone growth. All implants were electromechanically assessed under cyclic loads of 1000 N at 2 Hz, representing physiological lumbar loading. All three configurations produced at least as much power as the piezoelectric macro-fiber composites, validating the use of piezoelectric discs for this application. Future work is needed to characterize the electromechanical performance of commercially manufactured piezoelectric stacks under physiological lumbar loads, and mechanically assess the composite implants according to FDA guidelines for lumbar interbody fusion devices.

This paper deals with the analysis of active constrained layer damping (ACLD) of laminated thin composite panels using vertically and obliquely reinforced 1–3 piezoelectric composite materials as the material of the constraining layer of the ACLD treatment. A finite element model has been developed for analyzing the ACLD of laminated antisymmetric cross-ply and antisymmetric angle-ply thin composite panels integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuations of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed that the vertical actuation dominates over the in-plane actuation. Particular emphasis has been placed on investigating the performance of the patches when the orientation angle of the piezoelectric fibers of the constraining layer is varied in the two mutually orthogonal vertical planes. The analysis revealed that the vertically reinforced 1–3 piezoelectric composites which are in general being used for the distributed sensors can be potentially used for the distributed actuators of high performance light-weight smart thin composite panels.

This paper concerns the dynamic analysis of composite beams containing elastic and viscoelastic (VE) layers. A method for determination of the dynamic characteristics of multilayered beams with VE layers (i.e., natural frequencies, non-dimensional damping ratios and modes of vibration) is presented. The Euler–Bernoulli beam theory and the Timoshenko theory are used to describe the elastic and VE layers, respectively. To describe the mechanical properties of a VE layer, the four-parameter rheological model with fractional derivative is applied. A number of particular rheological models are particular cases of this general model. The virtual work principle and the finite element method together with the Laplace transform are used to derive the equation of motion in the frequency domain. The dynamic characteristics of a beam with VE layers are obtained as the solution to a properly defined nonlinear eigenvalue problem. The continuation method is adopted for solving the nonlinear eigenproblem. Several conclusions concerning the accuracy of the method and variability of results are presented on the basis of numerical studies.

The present work fills a gap on the postbuckling behavior of multilayer functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical and spherical shell panels resting on elastic foundations subjected to central pinching forces and pressure loadings. Based on a higher-order shear deformation theory and the von Karman’s nonlinear strain–displacement relations, the governing equations of the FG-GPLRC cylindrical and spherical shell panels are established by the principle of virtual work. The non-uniform rational B-spline (NURBS) based isogeometric analysis (IGA), the modified arc-length method and the Newton’s iteration method are employed synthetically to obtain nonlinear load–deflection curves for the panels numerically. Several comparative examples are performed to test reliability and accuracy of IGA and arc-length method in present formulation and programming implementation. Parametric investigations are carried out to illustrate the effects of dispersion type of the graphene platelet (GPL), weight fraction of the GPL, thickness of the panel, radius of the panel and parameters of elastic foundation on the load–deflection curves of the FG-GPLRC shell panels. Some complex load–deflection curves of the FG-GPLRC cylindrical and spherical shell panels resting on elastic foundations may be useful for future references.

Purpose. The main purpose of the work is to review and systematize metal structural for the production and repair of automobile parts, as well as analyze modern trends in their further development. Methodology. The main problems associated with metal structural materials today include the following: high density of materials, which increases the mass of the car, the consumption of fuel and lubricants and the amount of harmful emissions into the atmosphere; the need to ensure the strength and reliability of automobile structures; the need to ensure passive and active safety; the susceptibility of materials to corrosion, the scale of which can be judged by the fact that approximately 20 % of the steel produced in the world is used to cover losses from corrosion; the task of reducing the environmental load on the environment; the development of new materials that meet modern requirements; the selection and justification of structural materials for car parts; preparation for post-war reconstruction, the need to save resources. The following research methods were used in the work: theoretical research (classification, systematization), analysis and generalization of known scientific results, empirical methods (comparison, observation), experimental research (metallographic analysis, impact toughness testing). Findings. The current state and problems associated with metal structural materials are analyzed; it is shown that structural materials significantly affect the mass of the car, strength, reliability, corrosion resistance, fuel and lubricant consumption and the number of harmful emissions into the atmosphere. The analysis of structural carbon steels allows us to correctly formulate the requirements for steels of certain groups of automotive parts, and to select materials for the manufacture or repair of automobile parts, taking into account the properties of the material, purpose and operating conditions of automotive parts. Modern trends in the development of new materials for road transport are considered: high-strength steels, aluminum alloys, nanomaterials, composite materials. The possibilities of creating layered composite materials by explosion welding are investigated, and impact toughness tests are conducted. Originality. A comprehensive analysis of the problems of metal structural materials has been carried out, which allows us to identify their impact on the mass of the car, the consumption of fuel and lubricants and the number of harmful emissions into the atmosphere. The main trends in the development of metal structural materials have been highlighted; the approach to assessing materials according to the criterion of embodied energy has been considered. It is emphasized that the development of innovative technologies for creating new metal structural materials is an important step towards the transition to environmentally friendly transport in the country. The use of layered metal composite materials as materials with high fracture toughness has been substantiated. Practical value. An analysis of the main grades of structural carbon steels has been carried out, which allows us to correctly formulate the requirements for steels of certain groups of automotive parts, as well as to select materials for the manufacture and repair of automotive parts, taking into account the properties of steels, the purpose and operating conditions of automotive parts. The directions and problems of metal structural materials for automotive parts have been highlighted. Layered metal composite materials obtained by explosion welding have been proposed as materials with high fracture toughness.

A mathematical model is formulated for calculating the stress-strain state (SSS) of piezoelectric layered polymer composite materials (PCM) equipped with a control piezoactuator. The model implements the principle of thermo-piezoelectric analogy, which allows to move from the coupled boundary value problem of electroelasticity to the boundary value problem of thermoelasticity. The mathematical model was tested with a numerical calculation of the mechanical behavior of a sample structurally similar to a rotor blade, equipped with control piezo-actuators and made of equal strength and unidirectional fiberglass.

A possible failure mechanism in layered composite materials is delamination. This mechanism can be analysed numerically using the discontinuous solid-like shell element. In this element, the delamination crack can occur at arbitrary locations and is incorporated as a jump in the displacement field by using the partition-of-unity property of finite element shape functions. The performance of the element is demonstrated by a small example.

For future sonar transducer applications that emphasize the detection of acoustical signals in a hydrostatic mode, new piezoelectric composite materials have been developed. Ceramic-polymer composites having '1-3' and '0-3' connectivity patterns are shown to exhibit much higher sensitivities than conventional PZT ceramics. Glass-ceramic composites are free of aging, and have potential applications in standard transducers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Overall properties of piezoelectric composites with spring-type imperfect interfaces using the mechanics of structure genome

This paper reports on results of employing piezoelectric composites as sensors for detecting simulated damage events and monitoring dynamic and impact loads in composite structures. Two piezoelectric composite materials have been developed and characterized. The materials have been prepared by dispersing ceramic powder into a polymer matrix. Calcium modified lead titanate (PTCa) was used as the ceramic phase, while a non-polar epoxy resin, (Epon 828) and vinylidene fluoride trifluoroethylene (P(VDF-TrFE)), a polar copolymer, were used as the polymer matrix phases. PTCa/epoxy and PTCa/P(VDF-TrFE) composite materials were employed as embedded sensors in composite laminates to detect elastic waves propagating in such structures and to monitor transient applied loads. Furthermore, these materials could be used as sensors in health assessment techniques for composite materials where diagnostic waves methods are utilized.