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The purpose of this paper is to derive knockdown factor functions in terms of a shell thickness ratio (i.e. the ratio of radius to thickness) for conventional orthogrid and hybrid-grid stiffened cylinders for the lightweight design of space launch vehicles.

The shell knockdown factors of grid-stiffened cylinders under axial compressive loads are derived numerically considering various shell thickness ratios. Two grid systems using stiffeners – conventional orthogrid and hybrid-grid systems – are used for the grid-stiffened cylinders. The hybrid-grid stiffened cylinder uses major and minor stiffeners having two different cross-sectional areas. For modeling grid-stiffened cylinders with various thickness ratios, the effective thickness (t_eff) of the cylinders is kept constant, and the radius of the cylinder is varied. Thickness ratios of 100, 192 and 300 are considered for the orthogrid stiffened cylinder, and 100, 160, 200 and 300 for the hybrid-grid stiffened cylinder. Postbuckling analyses of grid-stiffened cylinders are conducted using a commercial nonlinear finite element analysis code, ABAQUS, to derive the shell knockdown factor. The single perturbation load approach is applied to represent the geometrical initial imperfection of a cylinder. Knockdown factors are derived for both the conventional orthogrid and hybrid-grid stiffened cylinders for different shell thickness ratios. Knockdown factor functions in terms of shell thickness ratio are obtained by curve fitting with the derived shell knockdown factors for the two grid-stiffened cylinders.

For the two grid-stiffened cylinders, the derived shell knockdown factors are all higher than the previous NASA’s shell knockdown factors for various shell thickness ratios, ranging from 100 to 400. Therefore, the shell knockdown factors derived in this study may facilitate in the development of lightweight structures of space launch vehicles from the aspect of buckling design. For different shell thickness ratios of up to 500, the knockdown factor of the hybrid-grid stiffened cylinder is higher than that of the conventional orthogrid stiffened cylinder. Therefore, it is concluded that the hybrid-grid stiffened cylinder is more efficient than the conventional orthogrid-stiffened cylinder from the perspective of buckling design.

The obtained knockdown factor functions may provide the design criteria for lightweight cylindrical structures of space launch vehicles.

Derivation of shell knockdown factors of hybrid-grid stiffened cylinders considering various shell thickness ratios is attempted for the first time in this study.

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.

This paper aims to present a new robustness-based design strategy for thin-walled composite structures under compressive loading, which combines strength requirements in terms of the limit and ultimate load with robustness requirements evaluated from the structural energy until collapse.

In order to assess the structural energy, the area under the load-shortening curve between several characteristic points such as local buckling, global buckling, onset of degradation and collapse load is calculated. In this context, a geometrically nonlinear finite element analysis is carried out, in which the ply properties are selectively degraded by progressive failure.

The advantage of the proposed methodology is observed by analyzing unstiffened composite plates under compressive loading, wherein the lightest plate that satisfies both strength and robustness requirements can be attained.

As a practical implication, this methodology gives a new argument to accept the collapse load close to the ultimate load once robustness is ensured.

The structural energy is employed to investigate the robustness of thin-walled composite structures in postbuckling, and new energy-based robustness measures are proposed. In the design of composite structures, this innovative strategy might lead to a more robust design when compared to an approach that only accounts for the ultimate load.

With the widespread use of the composites over other metallic materials in different fields of engineering, studies on damages of composite structures have assumed great importance. Among various kinds of damages, delamination is of very serious concern to composite applications. It may arise as a consequence of impact loading, stress concentration near a geometrical or material discontinuity or manufacturing defects. The presence of one or more delaminations in the composite laminate may lead to a premature collapse of the structure due to buckling at a lower level of compressive loading. So the effect of delamination on stability of composite structures needs attention and thus constitutes a problem of current interest. The purpose of this paper is to deal with both numerical and experimental investigations on buckling behaviour of single and multiple, delaminated, industry driven, woven roving glass/epoxy composite plates on clamped free clamped free (CFCF) rectangular plates.

For numerical analysis, a finite element model was developed with an eight noded two dimensional quadratic isoparametric element having five degrees of freedom per node. The elastic stiffness matrices were derived using linear first order shear deformation theory with a shear correction factor. Green's nonlinear strain equations are used to derive the geometric stiffness matrix. The computation of buckling load based on present formulation is compared with the experimental results for the effect of different parameters on critical load of the delaminated composite panels. In the experimental study, the influences of various parameters such as delamination area, fiber orientations, number of layers, aspect ratios on the buckling behaviour of single and multiple delaminated woven roving glass/epoxy composite plates were investigated. Buckling loads were measured by INSTRON 1195 machine for the delaminated composite plates.

Comparison of numerical results with experimental results showed a good agreement. Both the results revealed that the area of delaminations, fiber orientations, number of layers and aspect ratio have paramount influence on the buckling behaviour of delaminated plate.

The present study is part of Jayaram Mohanty's doctoral thesis, an original research work.

This bibliography contains references to papers, conference proceedings, theses and books dealing with finite strip, finite prism and finite layer analysis of structures, materially and/or geometrically linear or non‐linear.

Impact and fatigue are critical loading conditions for composite aerostructures. Compression behavior after impact and fatigue is a weak point for composite fuselage panels. The purpose of this paper is to characterize experimentally the compression behavior of carbon fiber reinforced plastic (CFRP) stiffened fuselage panels after impact and fatigue.

In total, three panels were manufactured and tested. The first panel was tested quasi-statically to measure the reference compression behavior. The second panel was subjected to impact so as to create barely visible impact damage (BVID) at different locations, then to fatigue and finally to quasi-static compression. Finally, the third panel was subjected to impact so as to create visible impact damage (VID) at different locations and then to quasi-static compression. The panels were tested using ultrasound inspection just after manufacturing to check material quality and between different tests to detect impact and fatigue damage accumulation. During tests the mechanical behavior of the panel was monitored using an optical displacement measurement system.

Experimental results show that the presence of impact damage significantly degrades the compression behavior of the panels. Moreover, the combined effect of BVID and fatigue was proven more severe than VID.

The paper gives information about the compression after impact and fatigue behavior of CFRP fuselage stiffened panels, which represent the most realistic loading scenario of composite aerostructures, and describes an integrated experimental procedure for obtaining such information.

The authors search the optimal distribution of bending flexure along the axis of the rod. For the solution of the actual problem, the stability equations take into account all possible convex, simply connected shapes of the cross-section. The authors study the cross-sections with equal principal moments of inertia. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The cross-section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. The optimal form of the cross-section is known to be an equilateral triangle. The distribution of material along the length of a twisted and compressed rod is optimized so that the rod must support the maximal moment without spatial buckling, presuming its volume remains constant among all admissible rods. The static Euler's approach is applicable for simply supported rod (hinged), twisted by the conservative moment and axial compressing force.

The optimization problems for stability of twisted and compressed rods are studied in this manuscript. The complement for Euler's buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under simultaneous torsion and compression (Greenhill, 1883).

For determining the optimal solution, the authors directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for simultaneously twisted and compressed rod is stated in closed form.

(1) The linear stability equations are applied. (2) No nonlinear or postbuckling effects were accounted. (3) The moment-free, ideal boundary conditions on both ends of the rod assumed.

One of the most common design cases in mechanical engineering is the concurrent compression and twisting of the straight members. The closed-form solution allows the immediate estimation of the optimization effect for axes and rotors in industrial and automotive engineering.

The application of lighter and material-saving structural elements allow the saving fabrication resources, reducing the mass of vehicles and industry machines. The systematic usage of material optimized structural elements assists the stabilization of global energy balance of Earth.

Albeit the governing ordinary differential equations are linear, the application of the optimality conditions leads to the nonlinearity of the final optimization equations. The search of closed form solution of the nonlinear differential equations is one of the mathematically hardest tasks in engineering mathematics. The closed-form solution presents in terms of higher transcendental functions.

The practical behaviour of problems exhibiting bifurcation with secondary branches cannot be studied in general by using standard path‐following methods such as arc‐length schemes. Special algorithms have to be employed for the detection of bifurcation and limit points and furthermore for branch‐switching. Simple methods for this purpose are given by inspection of the determinant of the tangent stiffness matrix or the calculation of the current stiffness parameter. Near stability points, the associated eigenvalue problem has to be solved in order to calculate the number of existing branches. The associated eigenvectors are used for a perturbation of the solution at bifurcation points. This perturbation is performed by adding the scaled eigenvector to the deformed configuration in an appropriate way. Several examples of beam and shell problems show the performance of the method.

The problems of inelastic instability (buckling) and dynamic instability (resonance) have been the subject of extensive investigation and have received wide attention from the structural mechanics community. This paper aims to tackle these problems in thin-walled structures, taking into account geometrical and/or material non-linearity.

The inelastic buckling mode interactions and resonance instabilities of prismatic thin-walled columns are analysed by implementing the semi-analytical finite strip method (FSM). A scalar damage parameter is implemented in conjunction with a material modelling named rheological-dynamical analogy to address stiffness reduction induced by the fatigue damage.

Inelastic buckling stresses lag behind the elastic buckling stresses across all modes, which is a consequence of the viscoelastic behaviour of materials. Because of the lag, the same column length does not always correspond to the same mode at the elastic and inelastic critical stress.

This paper presents the influence of mode interactions on the effective stresses and resonance instabilities in thin-walled columns due to the fatigue damage. These mode interactions have a great influence on damage variables because of the fatigue and effective stresses around mode transitions. In its usual semi-analytical form, the FSM cannot be used to solve the mode interaction problem explained in this paper, because this technique ignores the important influence of interaction of the buckling modes when applied only for undamaged state of structure

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.