Czesław Szymczak

Sensitivity analysis of thin-walled members, problems and applications

A review of problems related to sensitivity analysis of thin walled members with open monosymmetric or bisymmetric cross-section is presented. The restraints imposed on angle of cross-section rotation, transverse displacement and cross-section warping are taken into account. The consideration is based upon the classical theory of thin-walled beams with nondeformable cross-section. The first variations of state variables due to a change of the design variable are investigated. Arbitrary displacement, internal force or reaction of the member subject to static load, critical buckling load, frequency and mode of torsional vibration are assumed to be the state variables. The dimensions of the cross-section, the material constants, the restraints stiffness, and their locations, position of the member ends are taken as the design variables. Accuracy of the approximate changes of the state variables achieved by sensitivity analysis is also discussed.

On torsional buckling of thin walled I columns with variable cross-section

Abstract The problem of extreme critical conservative loads of torsional buckling for axially compressed thin walled I columns with variable, within given limits, bisymmetric cross-section, is considered. Basing on the Pontryagins maximum principle, it has been shown that the critical load of a column with variable cross-section may exceed the bounds defined by critical loads for columns with constant extreme cross-section. On the other hand the extreme loads for flexural buckling are the critical ones for columns with extreme constant cross-section. In the numerical example, enclosed, the extreme critical loads for simply supported I column with variable width of flanges and corresponding optimal shapes of flanges are the object of analysis. Moreover, it has been shown that these bifurcation points are symmetric and stable.

Optimal design of thin-walled I beams undergoing torsion

Abstract The problem of minimum volume design of a thin-walled I beam undergoing torsion is investigated. The behaviour of the beam is described in accord with the theory of thin-walled beams with nondeformable cross-section. The constraint conditions on normal stress level, the magnitude of rotational displacement at a specified cross-section and the extreme values of the cross-section dimensions variable along the beam axis are discussed. An iterative method of solution based upon the optimality condition derived with aid of Pontryagins maximum principle is developed. A numerical example of a cantilever I beam with variable width of flanges is presented.

On post-buckling behavior of columns with cubic constitutive equations

Abstract The critical flexural buckling load and the post-buckling behavior of a column made of a material with cubic constitutive equation is discussed. The solution of the problem given previously by Haslach [Int. J. Non-linear Mech. 20], 53, 1986 is improved. Some numerical examples for a wood column problem are given.

Local buckling of thin-walled channel member flange made of aluminum alloy

The paper deals with local stability of the thin-walled compressed flange of channel columns and beams made of aluminum alloy. The aim of paper is to find critical stress of local buckling of the flange member taking into account the web-flange interaction in linear and nonlinear elastic range of the member material. The governing differential equation of the problem is derived with aid of the principle of stationary total potential energy. The equation solution leads to the critical buckling stress and assessment of the number of half-waves in linear elastic range of the member material. Taking into account these results the analytical formula of the critical buckling stress in nonlinear elastic range is established using the tangent modulus theory and the Ramberg-Osgood stress-strain relationship. Finally the analytical results for simply supported members are compared with the FEM solutions and good agreement is observed.

Sensitivity analysis of thin-walled I-beams undergoing torsion

Abstract For thin-walled I-beams undergoing torsion, the first variations of an arbitrary internal force or a reaction or a displacement due to variations of the design variables are derived by using the solutions for primary and adjoint beams. The considerations are based on classical assumptions of the thin-walled beam theory. In a numerical example dealing with a cantilever I-beam, the coefficients determining the first variations of the support bimoment and the maximum angle of cross-section rotation due to a variation of flange width are presented. The effect of the axial load on the solutions obtained and an accuracy of estimation of change of internal forces and displacements by means of its first variations are also discussed.