An integrated framework for multi-criteria optimization of thin concrete shells at early design stages

Thin shells are crucially dependent on their shape in order to obtain proper structural performance. In this context, the optimal shape will guarantee performance and safety requirements, while minimizing the use of materials, as well as construction/maintenance costs.Thin shell design is a team-based, multidisciplinary, and iterative process, which requires a high level of interaction between the various parties involved, especially between the Architecture and Engineering teams. As a result of technological development, novel concepts and tools become available to support this process. On the one hand, concepts like Integrated Project Delivery (IPD) show the potential to have a high impact on multidisciplinary environments such as the one in question, supporting the early decision-making process with the availability of as much information as possible. On the other hand, optimization techniques and tools should be highlighted, as they fit the needs and requirements of both the shell shape definition process and the IPD concept. These can be used not only to support advanced design stages, but also to facilitate the initial formulation of shape during the early interactions between architect and structural engineer from an IPD point of view.This paper proposes a methodology aimed at enhancing the interactive and iterative process associated with the early stages of thin shell design, supported by an integrated framework. The latter is based on several tools, namely Rhinoceros 3D, Grasshopper, and Robot Structural Analysis. In order to achieve full integration of the support tools, a custom devised module was developed, so as to allow interoperability between Grasshopper and Robot Structural Analysis. The system resorts to various technologies targeted at improving the shell shape definition process, such as formfinding techniques, parametric and generative models, as well as shape optimization techniques that leverage on multi criteria evolutionary algorithms. The proposed framework is implemented in a set of fictitious scenarios, in which the best thin reinforced concrete shell structures are sought according to given design requirements. Results stemming from this implementation emphasize its interoperability, flexibility, and capability to promote interaction between the elements of the design team, ultimately outputting a set of diverse and creative shell shapes, and thus supporting the pre-design process.     

A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators: Bending and free vibrations

This paper addresses the bending and free vibrations of multilayered cylindrical shells with piezoelectric properties using a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elasticity theory. In the present 3D axisymmetric model, the equations of motion are expressed by expanding the displacement field using Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.     

Multiobjective optimization of a two-piece aluminum beverage bottle considering tactile sensation of heat and embossing formability

This paper deals with a multiobjective optimization of a screw-top beverage bottle for hot vending. The bottle body has temperate touch feeling and can be embossed easily by axially imposing a cylindrical tube die with rib-shaped inner surface on the outer surface of the bottle body. Initially, a contact nonlinear analysis of fingers grasping the bottle is carried out, and the amount of heat transmitted from the hot bottle to the flesh of the finger is then calculated to evaluate the hot touch feeling. Meanwhile, the simulation of the rib-shape embossing process of the bottle body is performed to evaluate the embossing formability of different rib shape designs. Finally, using response surface approximation method and weighted sum approach, a multiobjective optimization on the shape of the rib is performed to obtain temperate touch feeling as well as better embossing formability. The amount of heat transmitted from the optimized rib-shape embossed bottle decreased at least 30% as compared with that of the regular bottle.     

An exact solution for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends

In this paper, a new exact solution based on the classical shell theory (CST) for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends is proposed. The present exact solution can be summed up in the following steps: Firstly, the displacement functions are constructed by the governing differential equations with the exact closed form solutions; Then, the artificial spring technology is introduced to simulate the general boundary conditions of the two end edges of shell; Thirdly, the equation for natural frequencies is obtained by means of the method of reverberation-ray matrix (MRRM); Lastly, the vibration results are presented by the modified golden section search (MGSS) algorithm. By comparing the present method with published papers, the accuracy of present method is verified. On the basis of that, some new exact nature frequencies and mode shapes of the cross-ply laminated composite cylindrical shells with various classical boundary conditions and elastic restraints are performed and they can be served as the benchmark data for the future.     

Proposal and validation of an optimization method using Monte Carlo method for multi-objective functions

Solving optimization problems is essential for many engineering applications and research tools. In a previous report, we proposed a new optimization method, MOST (Monte Carlo Stochastic Optimization), using the Monte Carlo method, and applied it to benchmark problems for optimization methods, and optimization of neural network machine learning. While the proposed method MOST was a single objective, this study is an extension of MOST so that it can be applied to multi-objective functions for the purpose of improving generality. As the verification, it was applied to the optimization problem with the restriction condition first, and it was also applied to the benchmark problem for the multi-objective optimization technique verification, and the validity was confirmed. For comparison, the calculation by genetic algorithm was also carried out, and it was confirmed that MOST was excellent in calculation accuracy and calculation time.