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• The rigidity of an approximate Chebyshev gridshell with pin joints is calculated analytically. • A quantitative rigidity relation, K - EdRkn relation, which considers the influence of joint type and other gridshell parameters, is proposed. • The proposed K-EdnRk relation can give a fast and accurate prediction of the rigidity of a CEGS. Elastic gridshells (EGS) have many applications in the field of architecture. Built according to Chebyshev net geometry, the Chebyshev EGS (CGES) is a famous kind of EGS; since an arbitrary three-dimensional CEGS can be transformed into a planar state without any stretching strain. Due to its tremendous potential application in novelly deployed structures, the rigidity of CEGS is an important mechanical property to be investigated. In this study, using the analytical and finite element methods, the influence of joint types and gridshell parameters on the rigidity of CEGS subjected to point loads is studied in detail. The joint types are classified as pin joints, semi-rigidity joints, and rigid joints. A robust relation between rigidity and gridshell parameters is proposed, including Young's modulus, rod diameter, size of CEGS, joint stiffness, and rod numbers. Further, the above relation is nondimensionalized. The dimensionless rigidity is only related to the two dimensionless parameters, which are dimensionless joint stiffness and rod number. The rigidities of CEGS on four types of surfaces are calculated to verify the above relation, and satisfactory agreement is obtained. Therefore, the proposed relationship of rigidity is confirmed to be accurate and efficient for a wide range of parameters. [ABSTRACT FROM AUTHOR]

As an important impact energy absorber and a way to produce double-wall tubes, the inversion of the metal tube over a conical die is investigated in this study. Adopting the deformation profile inspired by FEM simulations, a theoretical model is proposed assuming the energy is dissipated by bending and compression in the meridional direction, and expansion in the circumferential direction. FEM simulations with a large range of geometrical parameters are used to validate the theoretical model, and results show that both the compressional force and the final circular radius of tube predicted by the theoretical model are quite accurate. Then, the energy dissipations along the axis of the tube by various mechanisms are analyzed in detail, and it is identified that the tube deformation in the thickness direction is the major reason of the current model’s deviation. Besides, the influence of the die radius, the friction between die and tube, as well as the dynamic effect are discussed. [ABSTRACT FROM AUTHOR]

In this study, the theoretical model of the expansion metal tubes reported in [1] is improved by considering the die radius r die . After the critical die radius r die * decided by the tube radius-thickness ratio and the conical angle of die is introduced, the tube expansions are classified into three different deformation modes, according to the relation between actual die radius r die and the critical die radius r die * . The detailed theoretical studies of these models are given in order to extend the applicability of the proposed theoretical model. Compared with the relevant experimental and finite element results, it is validated that the current model gives a more accurate steady compressional force, within a wide range of parameters, i.e., the tube radius-thickness ratio ≥ 20, and the die conical angle α ≤ 40° Besides, the expanded tube radius could be accurately predicted, which is important in the metal tube forming. The energy absorption abilities of the expansion tubes are then optimized by taking the tube material properties and friction into consideration. [ABSTRACT FROM AUTHOR]

As an important type of energy absorption devices, the expansion of metal tubes over a mandrel conical die are investigated by proposing a theoretical model, in which the deformation mechanism enlightened by finite element simulation is adopted. Different to the previous theoretical analysis that base on the momentum equations, the present model starts from the energy conservation point of view. That is, in the steady stage deformation of an expansion tube, the external work done by the compressional force should be dissipated by expansion in circumferential direction, bending in meridional direction, and friction. The theoretical model provides the predictions of steady compressional force and the tube radius after expansion, for rigid, perfectly plastic (R-PP) material, with or without strain hardening effect. Compared with the existing experimental data, and also the corresponding finite element simulations, the steady compressional force predicted by current theoretical analysis are both quite accurate. [ABSTRACT FROM AUTHOR]

Tensor skin is a kind of composite sandwich structure developed to improve the helicopter's crashworthiness when it impacts with water. In our previous theoretical studies, by employing the rigid, perfectly plastic idealization and the pulse approximation method, the static and dynamic responses of tensor skin under uniform pressure loading were obtained. In this study, a fluid–structure interaction simulation model of tensor skin impinging with water is established by FE method, in order to verify the previous theoretical analyses. It is found that the interaction pressure between the skin plate and water varies with the configuration of the plate. Compared with a solid plate, the pulses generated by a honeycomb-core sandwich plate and a tensor skin are more moderate. By studying the effect of water depth, the theoretical predictions of the tensor skin, as developed in our previous papers, are found valid for the deep water case. From the comparison among the theoretical predictions, pulse loading FE model, and the fluid–structure interaction FE model, the deviation of the theoretical prediction in the final deflection is found to be about 10% compared with that obtained from the fluid–structure interaction FE model. Thereby, the theoretical model and the pulse approximation method are confirmed to have sufficient accuracy for the design of tensor skins. [ABSTRACT FROM AUTHOR]

The inversion of a metal tube over a circular die is an important energy absorption device. Taking into consideration the curvature change during inversion process, this study proposes a two-dimensional theoretical model. Using rigid-perfectly plastic (R-PP) material idealization, its steady inversion load, curling radius after the tube׳s separation from the die, and the optimization of the die radius are analytically obtained based on energy conservation. Compared with the FE simulations, the current model greatly improves the prediction accuracy of the steady inversion force, with the deviation smaller than 10%. The prediction of the tube radius after inversion agrees well with the FE simulation and experimental data. Out of our expectation, the optimized die radius is found to be different from that of free inversion radius of the same tube. In this study, a simple formula of the optimized die radius is given. [ABSTRACT FROM AUTHOR]

Abstract: Comprised of cover ply, tensor ply and carrying ply, tensor skin is a kind of composite sandwich structure developed to improve the helicopter's crashworthiness in water impacts. In this study, a theoretical model is proposed to analyze the static and dynamic response of a kind of tensor skin. The whole response of tensor skin is divided into three stages: an elastic deformation stage of the whole beam; an unfolding stage of the tensor ply; and a stretching stage of the tensor ply. At the beginning of impact, the whole beam undergoes elastic deformation until the breakage of the cover and carrying plies; then the tensor ply left is unfolded and stretched to absorb more impact kinetic energy. In the unfolding stage, by adopting the rigid, perfectly plastic material idealization, a deformation mechanism with stationary plastic hinges is proposed. It is found that the static critical pressure first decreases then increases with the increasing central deflection. The static critical pressure varies with the geometric parameters, but the total energy dissipated in the unfolding stage is independent of the geometric parameters. The residual kinetic energy at the end of unfolding stage will be dissipated by the plastic stretching. The dynamic responses of the tensor skin are analyzed for step loaded pressure and rectangular pressure pulse. It is verified that the theoretical predictions display very good agreement with the corresponding finite element simulations. [Copyright &y& Elsevier]

Abstract: The free inversion of a metal tube can be applied in energy absorbing devices. The existing two-dimensional theoretical predictions on the knuckle radius and the steady load all displayed large discrepancy from the experimental observations. In this paper, with the rigid, perfectly plastic simplification, a three-dimensional analytical model is proposed based on the assumption of volume conservation and von Mises yield criteria, for quasi-static free inversion of circular tubes. A two-stage assumption on the thickness change is adopted, and the strain variation along the thickness direction is also considered. In order to validate the theoretical model, static inversion experiments are performed for aluminum tubes, and finite element calculations are also carried out for the elastic, perfectly plastic material. Compared with the experimental data and corresponding FE simulations, the current 3D model provides a better prediction on the steady inversion load than the previous 2D models. [Copyright &y& Elsevier]

This paper reports a finite element modeling approach to simulate the hypervelocity impact (HVI) response of composite laminate. Node–separation finite element (NSFE) method based on scalar–element–fracture technique for isotropic material in HVI simulation has been presented in the previous study. To extend NSFE to composite materials, an orthotropic node-separation finite element (ONSFE) method is developed. This approach employs an orthotropic continuum material model and a corresponding orthotropic–element–fracture technique to represent the HVI behavior/damage of composite laminate. A series of HVI simulations are conducted and the developed ONSFE method is validated by comparing with the experimental data. The simulation results show that ONSFE can successfully capture the HVI phenomena of composite laminate, such as the orthotropic property, nonlinear shock response, perforation, fiber breakage and delamination. Finally, a HVI event of Whipple shield is simulated and the computational capability of ONSFE for predicting the damage state of the composite bumper is further evaluated. [ABSTRACT FROM AUTHOR]

Large size and high precision inflatable membrane antenna is a promising design for space-based structures. To accurately control its mechanical states, such as shape and stress, the parameter sensitivity of an inflatable membrane antenna is theoretically investigated in this study. Based on the developed analytical matrix model, the influence of loading conditions (pressure, pre-stress) and material properties (elastic modulus, Poisson's ratio) is evaluated, and the stability of inflatable membrane antenna is also demonstrated analytically. Using Taylor expansion, an explicit closed-form solution is obtained, which avoids solving the transcendental equations. The solution is verified by corresponding orthogonal experiment technique and numerical simulations. The research shows that the influence of the variation of the factors on the mechanical states of inflatable membrane antenna will not be amplified, and the ranking of the factors' weights is elastic modulus = pressure > Poisson's ratio > pre-stress. [ABSTRACT FROM AUTHOR]

Thin-walled round tube systems are widely used in impact protection. However, in these systems, additional installation time and cost is required to constrain the tubes and prevent their splashing under impact loadings. To address this problem, a self-locked system comprised of thin-walled dumbbell-shaped tubes was recently proposed, which can prevent lateral splash from impact loadings without the presence of any constraints on the boundary or between the tubes. This paper provides a theoretical analysis on the deformation and collapse of dumbbell-shaped tubes under quasi-static lateral loads. A plastic hinge model is developed to estimate the force-displacement relationship, deformation efficiency and specific energy absorption of the dumbbell-shaped tube, and besides, an elastic solution is derived to describe the mechanical response of the dumbbell-shaped tube at small deformation. The theoretical models are validated by both finite element method (FEM) simulation and experiments. Based on the theoretical analysis, the effects of the geometry of the dumbbell-shaped tube on energy absorption are studied, and the optimal geometry design of the tube is discussed. The relation between each geometry parameter and energy absorption properties is summarized in a table, which provides important reference for designing dumbbell-shaped tubes in practical applications. [ABSTRACT FROM AUTHOR]