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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to develop an analytical approach to evaluate the influence of material uncertainties on cross‐sectional stiffness properties of thin walled composite beams.

Fuzzy arithmetic operators are used to modify the thin‐walled beam formulation, which was based on a mixed force and displacement method, and to obtain the uncertainty properties of the beam. The resulting model includes material uncertainties along with the effects of elastic couplings, shell wall thickness, torsion warping and constrained warping. The membership functions of material properties are introduced to model the uncertainties of material properties of composites and are determined based on the stochastic behaviors obtained from experimental studies.

It is observed from the numerical studies that the fuzzy membership function approach results in reliable representation of uncertainty quantification of thin walled composite beams. The propagation of uncertainties is also demonstrated in the estimation of structural responses of composite beams.

This work demonstrates the use of fuzzy approach to incorporate uncertainties in the responses analytically, in turn improving computational efficiency drastically as compared to the Monte‐Carlo method.

This study aims to analyse slender thin-walled anisotropic box-beams. Fiber-reinforced laminated composites could play an important role in the design of current and future generations of innovative civil aircrafts and unconventional unmanned configurations. The tailoring characteristics of these composites not only improve the structural performance, and thus reduce the structural weight, but also allow possible material couplings to be made. Static and dynamic aeroelastic stability can be altered by these couplings. It is, therefore, necessary to use an accurate and computationally efficient beam model during the preliminary design phase.

A proper structural beam scheme, which is a modification of a previous first-level approximation scheme, has been adopted. The effect of local laminate stiffness has been investigated to check the possibility of extending the analytical approximation to different structural configurations. The equivalent stiffness has been evaluated for both the case of an isotropic configuration and for simple thin-walled laminated or stiffened sections by introducing classical thin-walled assumptions and the classical beam theory for an equivalent system. Coupling effects have also been included. The equivalent analytical and finite element beam behaviour has been determined and compared to validate the considered analytical stiffness relations that are useful in the preliminary design phase.

The work has analyzed different configurations and highlighted the effect of flexural/torsion couplings and a local stiffness effect on the global behaviour of the structure. Three types of configurations have been considered, namely, a composite wing box configuration, with and without coupling effects; a wing box configuration with sandwich and cellular constructions; and a wing box with stiffened panels in a coupled or an uncoupled configuration. An advanced aluminium experimental test sample has also been described in detail. Good agreement has been found between the theoretical and numerical analyses and the experimental tests, thus confirming the validity of the analytical relations.

The equivalent beam behaviour that has been determined and the stiffness calculation procedure that has been derived could be useful for future dynamic and aeroelastic analyses.

The article presents an original derivation of the sectional characteristics of a thin-walled composite beam and a numerical/experimental validation.

The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section.

In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section.

The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables.

The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.

This paper aims to focus on the stochastic analysis of composite rotor blades with matrix cracking in forward flight condition.

The effect of matrix cracking and uncertainties are introduced to the aeroelastic analysis through the cross-sectional stiffness properties obtained using thin-walled beam formulation, which is based on a mixed force and a displacement method. Forward flight analysis is carried out using an aeroelastic analysis methodology developed for composite rotor blades based on the finite element method in space and time. The effects of matrix cracking are introduced through the changes in the extension, extension-bending and bending matrices of composites, whereas the effect of uncertainties are introduced through the stochastic properties obtained from previous experimental and analytical studies.

The stochastic behavior of helicopter hub loads, blade root forces and blade tip responses are obtained for different crack densities. Further, assuming the behavior of progressive damage in same beam is measurable as compared to its undamaged state, the stochastic behaviors of delta values of various measurements are studied. From the stochastic analysis of forward flight behavior of composite rotor blades at various matrix cracking levels, it is observed that the histograms of these behaviors get mixed due to uncertainties. This analysis brings out the parameters which can be used for effective prediction of matrix cracking level under various uncertainties.

The behavior is useful for the development of a realistic online matrix crack prediction system.

Instead of introducing the white noise in the simulated data for testing the robustness of damage prediction algorithm, a systematic approach is developed to model uncertainties along with damage in forward flight simulation.

The purpose of this paper is to consider divergence of composite plate wings as well as slender wings with thin-walled cross-section of small-size airplanes. The main attention is paid to establishing of closed-form mathematical solutions for models of wings with coupling effects. Simplified solutions for calculating the divergence speed of wings with different geometry are established.

The wings are modeled as anisotropic plate elements and thin-walled beams with closed cross-section. Two-dimensional plate-like models are applied to analysis and design problems for wings of large aspect ratio.

At first, the equations of elastic deformation for anisotropic slender, plate-like wing with the large aspect ratio are studied. The principal consideration is delivered to the coupled torsion-bending effects. The influence of anisotropic tailoring on the critical divergence speed of the wing is examined in closed form. At second, the method is extended to study the behavior of the large aspect ratio, anisotropic wing with box-like wings. The static equations of the wing with box-like profile are derived using the theory of anisotropic thin-walled beams with closed cross-section. The solutions for forward-swept wing with box-like profiles are given in analytical formulas. The formulas for critical divergence speed demonstrate the dependency upon cross-sectional shape characteristics and anisotropic properties of the wing.

The following simplifications are used: the simplified aerodynamic theory for the wings of large aspect ratio was applied; the static aeroelastic instability is considered (divergence); according to standard component methodology, only the component of wing was modeled, but not the whole aircraft; the simplified theories (plate-lime model for flat section or thin-walled beam of closed-section) were applied; and a single parameter that defines the rotation of a stack of single layers over the face of the wing.

The simple, closed-form formulas for an estimation of critical static divergence are derived. The formulas are intended for use in designing of sport aircraft, gliders and small unmanned aircraft (drones). No complex analysis of airflow and advanced structural and aerodynamic models is necessary. The expression for chord length over the span of the wing allows for accounting a board class of wing shapes.

The derived theory facilitates the use of composite materials for popular small-size aircraft, and particularly, for drones and gliders.

The closed-form solutions for thin-walled beams in steady gas flow are delivered in closed form. The explicit formulas for slender wings with variable chord and stiffness along the wing span are derived.

The purpose of the study was to develop the forming methodology for FML laminates with complex shapes, based on aluminium and epoxy-glass composite.

The subject of research encompassed Al/GFRP fibre metal laminates. Autoclave process has been selected for FML profiles production. The manufacturing process was followed by quality analysis for laminates produced.

The achievement of high stability and dimensional tolerance of thin-walled FML laminates is ensured by developed technology. The values of selected sections angles are significantly limited as a result of forming of FML laminates through the components performing. Failure to adhere to technological recommendations and to high regime of developer technology may lead to the occurrence of defects in FML.

Thin-walled composite structures could be applied in light-weight constructions, such as aircraft structures, which must meet rigorous requirements with regard to operation under complex load. The development of this type of technology may contribute to increased importance of FML sections in research area and finally to increased scope of their applications.

The production of thin-walled FML profiles with complex geometry, which would be characterized by dimensional stability and repeatable structural quality free of defects, is associated with many problems. No studies have been published so far on an effective forming process for FML laminates with complex shapes. Developed methodology has been verified through quality evaluation of produced profiles by means of non-destructive and destructive methods. The development of this type of technology may contribute to increased importance of FML, e.g. in aerospace technology.

This paper aims to present an evaluation method for energy-absorption characteristics of thin-walled composite structures with random uncertain parameters.

The mechanical properties of T700/3234 are obtained by material performance tests and energy-absorption results are obtained by quasi-static crushing tests of thin-walled composite circular tubes. The indicators of triggering specific load (TSL) and specific energy absorption (SEA) are introduced and calculated to determine the energy-absorption characteristics and validate the probability finite element analysis model. The uncertainty in the parameters contain the machining tolerance for the thickness and inner diameter of composite circular tubes and are associated with the composite material system. The Plackett–Burman method is used to choose the measurement parameters. Then, the response surface method is used to build a second-order function of random uncertain parameters versus TSL/SEA, and the Monte Carlo method is finally used to obtain the probabilities of TSL and SEA.

The finite element models can accurately simulate the initial peak load, load-displacement curve and SEA value. The random uncertain parameter method can be used to evaluate the energy-absorption characteristics of thin-walled composite circular tubes.

The presented evaluation method for energy-absorption characteristics of thin-walled composite structures is an approach that considers uncertain parameters to increase the simulation accuracy and decrease the computational burden.

This methodology considers uncertain parameters in evaluating the energy-absorption characteristics of thin-walled composite structures, and this methodology can be applied to other thin-walled composite structures.

Ensuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.

The present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.

The efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.

The experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

The purpose of this paper is to analyze and control the thermally induced vibration of orbiting smart satellite panels, which have been modeled as functionally graded material (FGM) beams.

It is assumed that the satellite moves in a circular orbit and has pitch angle rotation maneuver. Rapid temperature changes at day–night transitions in orbit generate time dependent bending moments that induce vibrations in the appendages. So, the heat radiation effects on the appendages should be considered. The thermally induced vibrations of the appendages and the nonlinear heat transfer equation are coupled and should be solved simultaneously. So, the governing equations of the motion are nonlinear and very complicated ones. A robust passivity-based controller is proposed to control the satellite maneuver and appendages vibrations, using piezoelectric sensors/actuators.

After the simulation, the effects of the heat radiation, piezoelectric actuators and piezoelectric locations on the response of the system are studied. The results of dynamic response and thermal analysis show that the radiation thermal effects are coupled with structure dynamic. These effects induce the vibration. Also, the effectiveness and the capability of the controller are analyzed. The results of the simulation show that the robust passivity-based control can ensure that the satellite rotates in the desired trajectory and vibrations of the appendages are damped. It demonstrates that the proposed control scheme is feasible and effective.

The paper is the basis of deriving the governing equations, thermal analysis and a robust control system design of a smart satellite with FGM panels.