Optimization of rigid-plastic geometrically nonlinear round plates of piecewise constant thickness

Purpose The purpose of this paper is to investigate the problem of optimizing geometrical and physical parameters of a stepped shell that maximize its rigidity and strength for given overall shell dimensions and fixed weight equal to the weight of a shell of constant thickness. Design/methodology/approach A mathematical model of the construction’s stress-strain state is described by solving a system of differential equations for each of the constituent parts of the shell, conjugation conditions on the division lines and boundary conditions. The stated optimization problem is reduced to a nonlinear programming problem, which is solved by the deformable polyhedron method in combination with the method of direct search and using the parallel computing package in the Wolfram Mathematica software application. Findings As follows from the results of the calculation, optimizing the shell parameters allows for a substantial increase in rigidity (decrease of the greatest deflection) and strength (increase of the load-carrying capacity) of the shell of constant stepwise thickness, as opposed to a shell of constant thickness, with constant weight and dimensions. Originality/value A problem of optimal design of a cylindrical composite panel of piecewise constant thickness is solved in the presented work. Numerical examples demonstrate that a substantial increase in rigidity and strength of a stepped composite shell can be achieved by the optimal choice of its geometrical and physical parameters.

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An Experimental-Numerical Method for Nonlinear Structural Mechanics

Journal of Applied Mechanics ◽

10.1115/1.2900996 ◽

1993 ◽

Vol 60 (4) ◽

pp. 875-882

Author(s):

F. J. M. Starmans ◽

W. A. M. Brekelmans ◽

J. D. Janssen

Keyword(s):

Structural Data ◽

Measured Data ◽

Geometrically Nonlinear ◽

The Finite Element Method ◽

Likelihood Estimator ◽

Rigid Plastic ◽

Material Points ◽

Nonlinear Rigid ◽

Plastic Case ◽

Nonlinear Structural Mechanics

A maximum likelihood estimator and the finite element method are used to construct a tool for estimating the state of continuous structures from measured structural data. These structural data can, for example, consist of displacements of material points and stresses or strains at material points. The statistical uncertainty of the measured data is supposed to be known. An approximation for the uncertainty of the estimated state can be given. The analyzing tool, elaborated for the geometrically nonlinear rigid plastic case, is useful for evaluation of feasibility and accuracy of experimental set-ups. An example of application of the tool is presented.

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Dynamic Stability of an Orthotropic Cylindrical Shell of Piecewise Constant Thickness under the Action of External Pulsating Pressure

Russian Aeronautics ◽

10.3103/s106879981902003x ◽

2019 ◽

Vol 62 (2) ◽

pp. 192-198 ◽

Cited By ~ 1

Author(s):

V. N. Bakulin ◽

A. Ya. Nedbai ◽

I. O. Shepeleva

Keyword(s):

Cylindrical Shell ◽

Dynamic Stability ◽

Orthotropic Cylindrical Shell ◽

Constant Thickness ◽

Piecewise Constant

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Vibration analysis of non-uniform porous beams with functionally graded porosity distribution

Proceedings of the Institution of Mechanical Engineers Part L Journal of Materials Design and Applications ◽

10.1177/1464420718780902 ◽

2018 ◽

Vol 233 (8) ◽

pp. 1678-1697

Author(s):

M Heshmati ◽

F Daneshmand

Keyword(s):

Mathematical Formulation ◽

Beam Theory ◽

Considerable Change ◽

Functionally Graded ◽

Mode Shapes ◽

Constant Thickness ◽

Thickness Variation ◽

Porosity Distribution ◽

Piecewise Constant ◽

Modes Of Vibration

In this paper, the effect of different profile variations on vibrational properties of non-uniform beams made of graded porous materials is studied. Timoshenko beam theory is used to present the mathematical formulation of the problem including shear deformation, rotary inertia, non-uniformity of the cross-section, and graded porosity of the beam material. Three different variations of porosities through the thickness direction are introduced. The beam is assumed with the clamped condition at both ends. To obtain a numerical solution, finite element formulations of the governing equations are presented. The non-uniform beam is approximated by another beam consisting of n elements with piecewise constant thickness to keep the volume and hence the total mass unchanged for each element. The beam response has been calculated for the first three modes of vibration. In each case, the results for different types of thickness variation and porosity distribution are compared with those obtained for a beam with uniform thickness. The effects of non-uniformity, taper parameters, and porosity distribution on the frequencies and mode shapes are investigated. It is observed that a considerable change in frequencies and mode shapes can be achieved by selection of different thickness variation and porosity distribution.

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