Tomasz Kubiak

Influence of Fibre Arrangement on the Buckling Load of Composite Plates - Analytical Solution

This paper deals with the problem of the influence of the angular arrangement of laminas on the buckling force of rectangular composite plates. The article presents a general, simple analytical method of buckling load determination and finding the best arrangement in terms of the highest stiffness in the prebuckling state. Some special characteristic cases of arrangements in an eight layered GFRP laminate are assumed, and buckling force as a function of the arrangement is investigated by finding proper maxima. Results for some characteristic lay-ups are compared with FEM and results found in literature.

Analytical–Numerical Method

The method proposed and explained below allows one to determine critical loads, natural frequencies and coefficients of the equation describing the postbuckling equilibrium path for thin orthotropic plates or girders, columns and beams composed of flat orthotropic plates (walls). This method also allows one to analyse a dynamic response of the plate structure subjected to pulse loading. Taking the deflections as a function of time and applying the relevant dynamic buckling criteria, it is possible to determine the dynamic critical load.

Influence of Boundary Conditions on the Critical and Failure Load in the GFPR Channel Cross-Section Columns Subjected to Compression

Thin-walled structures are widely used in building structures such as thin-walled vessels or storage tower, beam-columns of houses and halls, as components for cars, boats or airplanes and in sport industry. These types of structures are made not only as steel, but nowadays of composite materials.This paper deals with buckling and postbuckling behaviour and presents the experimental results for thin-walled composite columns with channel cross-section subjected to compression.

Numerical model of postbuckling behavior of GFRP beams subjected to pure bending

ABSTRACT This article deals with numerical calculations of thin-walled composite laminate beams with closed cross-section subjected to pure bending. Thin-walled beams with square cross-section made of eight-layer GFRP laminate have been taken into consideration. An FEM model has been prepared using four-node multi-layered shell elements governed by first-order shear deformation theory. Linear buckling analysis and nonlinear static analysis including large displacements have been performed. A Newton–Rapson algorithm has been employed. The FEM calculations have been conducted using Ansys® software. Three following layer arrangement were considered: [45/−45/0/0]S, [45/−45/45/0]S and [45/−45/45/0/0/−45/45/−45]T. The influence of number of load steps and geometrical initial imperfection on course of equilibrium paths has been checked. The results of calculations have been compared with experimentally performed four-point bending tests. Comparing results of tests and numerical calculations, it was observed that, in some cases, the deflection of beams does not correspond to the bifurcation buckling mode but corresponds to the lowest buckling load; the geometrical imperfection that corresponds to the higher buckling mode should be taken into consideration to obtain similar postbuckling equilibrium paths from tests and FEM calculations. As is well known, the buckling load and failure load for real structures depend on course of equilibrium paths. Taking above considerations into account, the author of this article tries to show some problems in obtaining numerical calculations results that are similar to experimental tests.

Thin-Walled Girders Subjected to Combined Load

This chapter deals with dynamic response of thin-walled girders subjected to combined load (bending and/or twisting). The load was assumed as stepped dynamic pulse of finite duration. Numerical analysis was conducted with finite element method (FEM). Analysis has concentrated on thin-walled girders of length 200 mm and squared cross-section (100 × 100 mm) with 1 mm wall thickness. Different numerical models were compared and investigation of dynamic response of the structure under combined load was performed for different boundary conditions. The critical values of load were determined according to well-known criteria (Volmir, Budiansky-Hutchinson and Ari-Gur-Simonetta criterion).

Theory of Thin Plates for Laminates

Thin isotropic, orthotropic or laminate plates with constant or widthwise variable material properties are considered in this monograph. Thin-walled beam-columns or girders composed of the above-mentioned plates are also analysed. In order to take into account all buckling modes (global, local and their interaction), the plate two-dimensional theory has been adopted to model the structures under analysis.

Thin-Walled Girders Subjected to Torsion

The results of the dynamic buckling analysis of girders subjected to torsion are presented in this chapter. All the results of numerical calculations to be discussed further were obtained with finite element method commercial software. Girders with square cross-sections and different lengths were considered. A little attention is paid to thin-walled structures with flat wall subjected to bending or torsion. It was therefore decided to fill this gap by conducting an analysis of thin-walled girders with closed cross-section and behaviour of such structures subjected to torsion impulse of finite duration.

Finite Element Method

The finite element method is used here to validate the analytical–numerical method presented in Chap. 3. The basic assumption and the used equations for thin plates in both the methods (ANM—the analytical–numerical method, FEM—the finite element method) are identical, but the way of solution is different. To apply a program based on the finite element method as a numerical experiment, confirming or validating the theoretical analysis or the analysis based on the analytical–numerical method, it is important to create an appropriate model. A properly chosen finite element type, a rational mesh density and appropriate boundary conditions play a significant role in obtaining the calculation results close to the reality.

Thin-Walled Columns

The chapter deals with static buckling, postbuckling behaviour and dynamic buckling of thin-walled column with open cross-section made of isotropic and orthotropic material. The analysed columns were subjected to compressed load. The results was obtained using finite element method and analytical-numerical method.

Girders, Beams Subjected to Pure Bending

In this chapter, the behaviour of girders or beams subjected to pulse load causing pure bending is presented. Girders with square cross-sections and beams with channel sections are considered. The part of multi-segment girders between two diaphragms is taken into account. The structures under analysis are made of isotropic or orthotropic material. The calculations were made with finite element method software and analytical-numerical method—the obtained results were compared.