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The optimization of variable thickness plates and shells is studied. In particular, three types of shell are considered: hyperbolic paraboloid, conoid and cylindrical shell. The main objective is to investigate the optimal thickness distributions as the geometric form of the structure changes from a plate to a deep shell. The optimal thickness distribution is found by use of a structural optimization algorithm which integrates the Coons patch technique for thickness definition, structural analysis using 9‐node Huang‐Hinton shell elements, sensitivity evaluation using the global finite difference method and the sequential quadratic programming method. The composition of the strain energy is monitored during the optimization process to obtain insight into the energy distribution for the optimum structures. Several benchmark examples are considered illustrating optimal thickness variations under different loading, boundary and design variable linking conditions.

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly developed linear, quadratic, and cubic, variable thickness, C(0) elements based on axisymmetric Mindlin‐Reissner shell theory. An integrated approach is used to carry out the whole shape optimization process in a fully automatic manner. A robust, versatile and flexible mesh generator is incorporated with facilities for generating either uniform or graded meshes, with constant, linear, or cubic variation of thickness, pressure etc. The midsurface geometry and thickness variations of the axisymmetric shell structure are defined using cubic splines passing through certain key points. The design variables are chosen as the coordinates and/or the thickness at the key points. Variable linking procedures are also included. Sensitivity analysis is carried out using either a semi‐analytical method or a global finite difference method. The objective of the optimization is the weight minimization of the structure. Several examples are presented illustrating optimal shapes and thickness distributions for various shells. The changes in the bending, membrane and shear strain energies during the optimization process are also monitored.

The main objective of this study is to develop a numerical model based on Isogeometric Analysis to study the dynamic behavior of multi-directional functionally graded plates with variable thickness.

A numerical study was conducted on the dynamic behavior of multi-directional functionally graded plates. Rectangular and circular plates with variable thickness are taken into investigation. The third-order shear deformation plate theory of Reddy is used to describe the displacement field, while the equation of motion is developed based on the Hamilton's principle. Isogeometric Analysis approach is employed as a discretization tool to develop the system equation, where NURBS basis functions are used. The famous Newmark method is used to solve time-dependent problems.

The results obtained from this study indicated that the thickness gradation has a more considerable effect than in-plane variation of materials in MFGM plates. Additionally, the influence of the damping factor is observed to affect the vibration amplitude of the plate. The results obtained from this study could be used for future investigations, where the viscous elasticity and other dynamic factors are considered.

Although there have been a number of studies in the literature devoted to analyzing the linear static bending and free vibration of FGM and MFGM plates with variable thickness, the study on dynamic response of FGM and MFGM plate is still limited. Therefore, this study is dedicated to the investigation of the dynamic behavior of multi-directional functionally graded plates.

In the current manuscript, the authors examine the Belleville spring with the variable thickness. The thickness is assumed to be variable along the meridional and parallel coordinates of conical coordinate system. The calculation of the Belleville springs includes the cases of the free gliding edges and the edges on cylindric curbs, which constrain the radial movement. The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations.

In the current manuscript, the authors examine the Belleville spring with the variable thickness. The calculation of the Belleville springs investigates the free gliding edges and the edges on cylindric curbs with the constrained radial movement. The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations.

The developed equations demonstrate that the shift of the inversion point to the inside edge does not influence the bending of the cone. On the contrary, the character of the extensional deformation (circumferential strain) of the middle surface alternates significantly. The extension of the middle surface of free gliding spring occurs outside the inversion. The middle surface of the free gliding spring squeezes inside the inversion point. Contrarily, the complete middle surface of the disk spring on the cylindric curb extends. This behavior influences considerably the function of the spring.

A slotted disk spring consists of two segments: a disk segment and a number of lever arm segments. Currently, the calculation of slotted disk spring is based on the SAE formula (SAE, 1996). This formula is limited to a straight slotted disk spring with freely gliding inner and outer edges.

The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations. The developed method is applicable for disk springs with radially constrained edges. The vertical displacements of a disk spring result from an axial load uniformly distributed on inner and outer edges. The method could be directly applied for calculation of slotted disk springs.

The nonlinear governing equations for the of Belleville spring centres were derived. The equations describe the deformation and stresses of thin and moderately thick washers. The variation method is applicable for the disc springs with free gliding and rigidly constrained edges. The developed method is applicable for Belleville spring with radially constrained edges. The vertical displacements of a disc spring result from an axial load uniformly distributed on inner and outer edges.

The purposes of this work were to determine: whether thickness of single layers can be used to accurately predict thickness and thermal resistance of multiple layer assemblies; and to identify variables affecting the total thickness (i.e. textile plus air layers) of bedding during simulated use. Thickness was determined when: materials were flat; and arranged over an infant manikin simulating use. Thermal resistance was measured using a guarded‐hotplate similar to that specified in ISO 11092:1993(E). During simulated use, the site of measurement, body position, tucking, and product type significantly affected thickness of bedding. Equations for predicting thickness and thermal resistance (dry) of multiple‐layer materials are described. While it was possible to predict thickness and thermal resistance of flat bedding from estimated values, extrapolation to bedding during simulated use was considered inappropriate, with significant differences of over 1,000 per cent.

This paper deals with the optimum design of composite laminated plates. Both ply orientation angles and ply thicknesses of the composite plate are used as design variables. The optimum design process is divided into two sublevels. In the first sublevel, the strain energy of the plate is minimized by changing the ply orientation angles while the ply thickness distributions remain unmodified. In the second sublevel, with the angle values obtained in the first sublevel, the optimum thickness distribution of each ply is obtained by minimizing the structural weight while satisfying stiffness and gauge constraints. The final optimum design is achieved by iterating between these two sublevels. The stiffness analysis is performed by the finite element method in which a triangular element is used that is suitable for from thin to thick plates and includes the transverse shear effects. All the derivative analysis is performed analytically. The mathematical programming method called Constrained Variable Metric is used to solve the optimum problem. An example is provided for a rectangular laminated plate with good results to show the effectiveness of the method.

The present findings report a significant influence of disc profile and thickness on the order of excitation leading to critical speed condition. Certain transverse modes of vibration of the disc have been obtained to be more susceptible to get excited while recording the lowest critical speeds.

Numerical simulation using finite-element method has been adopted due to the complicated geometry, complex loadings and intricate analytical formulation. A comprehensive analysis of exclusive as well as combination of thermal and centrifugal loads has been taken up to determine the intensity and characteristics of the individual/combined effects.

The typical gas turbine disc profile has been analyzed to predict the critical speed under the factual working condition of an aero-engine. FEM analysis of uniform and variable thickness discs have been carried out under stationary, rotating and rotating-thermal considerations while emphasizing the effect of disc profile and thickness. Centrifugal stresses developed due to rotational effect result in unceasing stiffening of the discs with higher stiffening for a greater number of nodal diameters. On the other hand, a role reversal of thermal effect from stiffening to softening is figured out with increasing numbers of nodal diameters. However, the discs are subjected to an overall stiffening effect on account of the combined centrifugal and thermal loading, with the effect decreasing with an increase in disc thickness. Under the combined loading, the order of excitation leading to critical speed condition is dependent on disc profile and thickness. Moreover, the vibrational modes (0,1) and (0,2) are identified as more prominent adverse modes corresponding to lowest critical speeds.

The present findings are expected to serve as guidelines during the design phase of gas turbine discs of aeroengine applications.

The present work deliberates on the simulation and analysis of gas turbine disc specific to aeroengine application. The real-life disc geometry has been analyzed with due consideration of major factual operating conditions to identify the critical speed. The identification of various critical speed using numerical analysis can help to reduce the number of experimental tests required for certification.

This paper deals with structural shape optimization of vibrating prismatic shells and folded plates. The finite strip method is used to determine the natural frequencies and modal shapes based on Mindlin‐Reissner shell theory which allows for transverse shear deformation and rotatory inertia effects. An automated optimization procedure is adopted which integrates finite strip analysis, parametric cubic spline geometry definition, automatic mesh generation, sensitivity analysis and mathematical programming methods. The objective is to maximize the fundamental frequency by changing thickness and shape design variables defining the cross‐section of the structure, with a constraint that the total volume of the structure remains constant. A series of examples is presented to highlight various features of the optimization procedure as well as the accuracy and efficiency of finite strip method.

Binder jetting is one of the essential additive manufacturing methods because it is cost-effective, has no thermal stress problems and has a wide range of different materials. Using binder jetting technology in the industry is becoming more common recently. However, it has disadvantages compared to traditional manufacturing methods regarding speed. This study aims to increase the manufacturing speed of binder jetting.

This study used adaptive slicing to increase the manufacturing speed of binder jetting. In addition, a variable binder amount algorithm has been developed to use adaptive slicing efficiently. Quarter-spherical shaped samples were manufactured using a variable binder amount algorithm and adaptive slicing method.

Samples were sintered at 1250°C for 2 h with 10°C/min heating and cooling ramp. Scanning electron microscope analysis, surface roughness tests, and density calculations were done. According to the results obtained from the analyzes, similar surface quality is achieved by using 38% fewer layers than uniform slicing.

More work is needed to implement adaptive slicing to binder jetting. Because the software of commercial printers is very difficult to modify, an open-source printer was used. For this reason, it can be challenging to produce perfect samples. However, a good start has been made in this area.

To the best of the authors’ knowledge, the actual use of adaptive slicing in binder jetting was applied for the first time in this study. A variable binder amount algorithm has been developed to implement adaptive slicing in binder jetting.

Over the last several years, the range of applications of photopolymerization process has been steadily increasing, especially in areas such as rapid prototyping, UV inks, UV coats and orthodontic applications. In spite of this, there are still several challenges to be overcome when the application concerns materials with thick layers. In this context, the main goal of this work is to outline a scheme to optimize the process of photopolymerizarion for thick layers, identifying its differences in relation to those applicable for thin layers.

For this research, the authors have applied multivariable analysis methods which allow the identification of principal conclusions, based on analytical and experimental results. For analytical analysis, the authors applied numerical optimization for multivariables, while experimental analysis was done based on design of experiments. Both the analyses were based on methyl methacrylate as monomer and Omnirad 2500 as photoinitiator, with the adjustable variables being initiator concentration; power of light source; light wave length; and thickness of layer. The range of values chosen for initiator concentration was between 1 and 10 per cent, while for light power, the range was 5‐9 W. For light wave length, the authors selected 325 and 400 nm as limits for their study and 0.12 and 4 mm as the range for thickness of layers. For the analytical approach of their study, it was possible to identify optimum conditions for curing thick layers, besides looking at optimum condition at each step along the varying thickness. On the other hand, in the experimental approach, the authors just considered the initiator concentration and thickness as variables, applying gravimetric and photometric analysis to determine the conversion curve of material.

In conclusion based on these studies, it was possible to identify the influence of thickness and initiator concentration as function of penetration depth, polymerization rate and homogeneity of material, in addition to determining the effect of light power and light wave length over the process. As a result of these studies, it was possible to identify situations wherein the material will possibly undergo a high degree shrinkage in addition to showing consequences of high quantity of initiator. On the other hand, low concentration of initiator is shown to provide more homogeneous solution besides being more suitable for deep layers. It was also possible to compare analytical and experimental results, making it possible to predict the behaviour of material for other conditions.

The main value of this work is to show the possibility of optimizing photopolymerizable systems through an analytical approach. In addition, it emphasized the viability of the application of UV curable material for producing moulded parts.