International Journal of Structural Stability and Dynamics

This work presents highly accurate numerical calculations of the buckling loads for thin elastic rectangular plates with known constant in-plane stresses, and in-plane shear loading that is increased until the critical load is obtained and the plate losses its stability. The solutions are obtained using the multi-term extended Kantorovich method. The solution is sought as the sum of multiplications of two one-dimensional functions. In this method a solution is assumed in one direction of the plate, and this enables transformation of the partial differential equation of the plate equilibrium into a system of ordinary differential equations. These equations are solved exactly by the exact element method, and an approximate buckling load is obtained. In the second step, the derived solution is now taken as the assumed solution in one direction, and the process is repeated to find an improved buckling load. This process converges with a small number of solution cycles. For shear buckling this process can only be used if two or more terms are taken in the expansion of the solution. Many examples are given for shear buckling loads for various cases of tension and compression bi-directional loading.

Description is given for a finite strip method for analyzing the large deflection response of simply supported rectangular functionally graded plates under normal pressure loading. The material properties of the functionally graded plates are assumed to vary continuously through the thickness of the plate, according to the simple power law and exponential law distribution. Both distributions of material properties are used to examine the stress variations. The fundamental equations for rectangular plates of functionally graded material (FGM) are obtained by discretizing the plate into some finite strips, which are developed by combining the Von–Karman theory for large transverse deflection and the concept of functionally graded material. The solution is obtained by the minimization of the total potential energy. The Newton–Raphson method is used to solve the non-linear equilibrium equations. Numerical results for square functionally graded plates are given in dimensionless graphical forms, and compared to the available results, wherever possible. The effects of material properties on the stress field through the thickness and on the variation of the central deflection at a given value of normal pressure loading are determined and discussed.

This paper presents a special thin-walled plane beam finite element that accounts for the in-plane cross-section local deformation. The element is based on the superposition of a classical beam displacement field and of an additional field describing local effects, with an approximation on the local second-order membrane stress field. The theoretical formulation is summarized and an application of the resulting numerical tool to the post-buckling analysis of RHS thin-walled members with moderate local and global slenderness susceptible to both global and local buckling is then performed. Different types of analyses are presented (computation of critical bifurcation loads, geometrically non-linear analysis, geometrically and materially non-linear analysis). The results obtained with the proposed beam finite element are compared to values provided by shell FE models.

This paper presents the incorporation of shear deformation effects into a Generalized Beam Theory (GBT) developed to analyze the structural behavior of composite thin-walled columns made of laminated plates and displaying arbitrary orthotropy. Unlike other existing beam theories, the present GBT formulation incorporates in a unified fashion (i) elastic coupling effects, (ii) warping effects, (iii) cross-section in-plane deformation and (iv) shear deformation. The main concepts and procedures involved in the available GBT are adapted/modified to account for the specific aspects related to the member shear deformation. In particular, the GBT fundamental equilibrium equations are presented and their terms are physically interpreted. An I-section is used to illustrate the performance of GBT cross-section analysis and the mechanical properties are explained in detail. With the purpose of solving the GBT system of differential equilibrium equations, a finite element formulation is briefly presented. Finally, in order to clarify the concepts involved in the formulated GBT and illustrate its application and capabilities, the linear (first-order) and stability behavior of three composite I-section members displaying non-aligned orthotropy are analyzed and the results obtained are thoroughly discussed and compared with estimates available in the literature.

In the framework of passive control devices for the seismic protection of new and existing buildings, large attention is getting more focused on Steel Plate Shear Walls (SPSW). Such a system, which is characterized by the use of slender steel panels, has been largely adopted in the last few years both in the North America and Japan. The structural behavior of slender shear walls is strongly conditioned by buckling phenomena, which may have a significant influence also on the ultimate strength of the system, despite the development of stable post-critical behavior due to tension field mechanism. In order to assess the influence of the geometry on the structural behavior of shear plates, in this paper, the theoretical behavior of steel panels in shear, based on existing simplified methodologies (PFI method and strip model theory) is analyzed and then compared to the results obtained by an extensive numerical study carried out by means of accurate finite element models. The comparison between theoretical and numerical results has been developed with reference to different values of the thickness and by varying the aspect ratio of the plate. In addition, the influence of intermediate stiffeners is investigated. On the whole, the obtained results provide useful information for the correct design of slender steel plates in shear to be used as stiffening and strengthening devices in new and existing framed structures.

The inevitable deviations from the nominal data of the resistance parameters have to be included in a numerical calculation of the load-bearing capacity of shells, because these structures are very imperfection-sensitive. The assumed imperfections are fundamental for the numerical buckling strength verification, because they have to cover the influence of all accidental imperfections of the structure in a consistent manner. Consistent equivalent geometric imperfections have been developed during the last years for the basic buckling cases of the circular cylindrical steel shell. The situation at shells subject to combined loading is more difficult, because not so much experimental data is available. Fundamental problems and previous proposals for assuming equivalent imperfections at combined loading are discussed in the contribution. In particular, it is a moot point whether the equivalent geometric imperfections have to be chosen without regard to the load case, because imperfections of real shells are caused by manufacturing and not by loading. Reasons are given for, why this is not applicable at equivalent imperfections of a numerical simulation. The conception of quasi-collapse-affine imperfections, which has already been proved at the basic buckling cases, can also be applied to shells under combined loading.

The purpose of this contribution is to investigate the stabilizing influence of hydrostatic fluid and/or gas pressure supports (especially the effect of the volume dependency on gas or fluid pressures) on the stability, namely the eigenvalues and eigenmodes of the stiffness matrix of shell or membrane-like structures undergoing large displacements. For this purpose, an analytical mesh free or lumped parameter description for the fluid/gas (see also Refs. 3, 12, 13 and 14) is taken, which yields a special structure of the nonlinear equations representing the change of the gas or fluid volume or alternatively the change of the wetted part of the shell surface. Finally this procedure leads to a stiffness matrix with several rank updates — depending on the volume containing either gas or fluid or both. These rank updates are a key part in the stability analysis: they describe the different coupling of the fluid or gas volume change with the structural displacements in addition to the deformation dependence of the standard pressure. The specific rank updates allow the derivation of a very efficient algorithm to compute the modifications of the eigenvalues and eigenmodes of the original stiffness matrix without gas or fluid loading or support.

The aircraft and space industry strives for significantly reduced development and operating costs. Reduction of structural weight at safe design is one possibility to reach this objective which is aimed by the following two running research projects: the EC project "COCOMAT" and the ESA study "Probabilistic Aspects of Buckling Knock Down Factors". These projects develop improved concepts and tools for a fast and reliable simulation of the buckling and the postbuckling behavior of thin-walled structures up to collapse, respectively, which allow the exploitation of considerable reserves in primary fibre composite structures in aerospace applications. For the validation of the concepts and tools, a sound database of experiments is needed which is also performed within these projects. This paper focuses on the experimental activities within these projects performed at the buckling test facility of the Institute of Composite Structures and Adaptive Systems (DLR). It presents an overview about the DLR buckling, postbuckling and collapse tests which are already finished and gives an outlook to the results which are expected until the end of the running projects. This paper explains the working of the buckling test facility, the advanced measurement systems, which are running in parallel to the tests, and gives exemplarily two test results. The structures considered are unstiffened cylinders (ESA study) as well as panels, which are understood as sections of cylinders, stiffened by stringers (COCOMAT project). The unstiffened cylinders are more related to space applications (e.g. Ariane busters or parts of the international space station ISS) and the stiffened panels focus more on aircraft structures (e.g. fuselage). The load case considered for all investigations presented in this paper is axial compression under static loading although the test facility is also ready to apply torsion and internal pressure, as well as dynamic axial impact.