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The purpose of this paper is to present the multi-objective optimization of the dynamic response of isotropic and laminated composite folded plates. The dynamic analysis has been carried out using the finite element method based on the first-order shear deformation theory.

Hamilton’s principle has been employed for the derivation of the governing equations. Natural frequencies are obtained using the eigenvalue extraction method. The optimal combination of the crank angle, lamination scheme and boundary conditions on the natural frequencies of folded plates for their safe and optimal dynamic design has been obtained. The analysis has been carried out using finite element approach based on FSDT to obtain the dynamic equation of single- and double-fold laminated plates. In total, 15 experiments as per Taguchi’s standard L₁₅ orthogonal array have been performed. Further, standard deviation (SD) based TOPSIS method is used to perform multi-response optimization of folded plates in order to rank the combination of the input parameters.

SD integrated with TOPSIS reveals that Experiment No. 8 (crank angle=90° and anti-symmetric lamination scheme=0°/90°/0°/90°), Experiment No. 14 (crank angle=150° and anti-symmetric lamination scheme=0^o/90^o/0^o/90^o), Experiment No. 2 (crank angle=30° and anti-symmetric lamination scheme=0°/90°/0°/90°) and Experiment No. 3 (crank angle=30° and symmetric lamination scheme=0°/90°/0°/90°) occupy rank 1 for one fold, one end clamped, one fold, two ends clamped, two folds, one end clamped and two folds, two ends clamped conditions, respectively, in order to maximize the modal response corresponding to the fundamental mode.

SD-based technique for order of preference by similarity to ideal solution (TOPSIS) method is used to rank the process parameters. The optimum combination of the input parameters on the multi-response optimization of dynamics of the folded plates has also been evaluated using the analysis of mean (ANOM).

This paper deals with the buckling analysis of prismatic folded plate structures supported on diaphragms at two opposite edges. The analysis is carried out using variable thickness finite strips based on Mindlin‐Reissner assumptions which allow for transverse shear deformation effects. The theoretical formulation is presented for a family of C(0) strips and the accuracy and relative performance of the strips are examined. Results are presented for a series of problems including plates and stiffened panels. In a companion paper these accurate and inexpensive finite strips are used in the context of structural shape optimization.

‘Shear‐constraints’ can be used to produce efficient Mindlin/Reissner or ‘discrete Kirchhoff’ bending elements. The paper shows that ‘selective shear‐constraints’ can be used to produce an effective formulation for folded‐plated structures.

An analysis of the plate and folded plate structures is carried out, taking into account the geometrical non‐linearities and the effects of creep, using the finite strip method. An assumption is made that only small deformations and large displacements and rotations exist. Creep of concrete has an important influence on some structures and cannot be neglected in such analysis, especially when geometrical non‐linearities are taken into account. The stiffness matrices (classical and geometrical) and the vector of equivalent nodal loading for the finite strips are obtained using the variation approach. The interpolation functions used are multiples of polynomial and trigonometric functions. Numerical examples showing the theoretical considerations are presented.

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.

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.

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 is given. The bibliography at the end of the paper contains 1,726 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 1996‐1999.

This paper 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 bibliography at the end of the paper contains more than 1330 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 1999–2002.

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates.

Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function.

The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered.

This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

Folding cartons are used in myriad consumer products. For some products, such as hair dye kits, a very high-resolution printing is required. This is typically done using a technology known as Gravure printing. Gravure printing utilizes engraved cylinders which are very expensive. As a result, the printer often combines multiple products on one set of cylinders to minimize the total number of cylinders used. Since the demand between products varies, this can result in overproduction of the low demand products. This chapter presents an integer programming formulation that assigns products across multiple sets of cylinders in order to minimize this overproduction. Sample problems, their solutions and solution times are presented.