Refinements on Gap Functions and Optimality Conditions for Vector Quasi-Equilibrium Problems via Image Space Analysis

By means of some new results on generalized systems, vector quasi-equilibrium problems with a variable ordering relation are investigated from the image perspective. Lagrangian-type optimality conditions and gap functions are obtained under mild generalized convexity assumptions on the given problem. Applications to the analysis of error bounds for the solution set of a vector quasi-equilibrium problem are also provided. These results are refinements of several authorsâ\u80\u99 works in recent years and also extend some corresponding results in the literature

Implementation Theory

This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered

A partitioned model order reduction approach to rationalise computational expenses in multiscale fracture mechanics

We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No \textit{a priori} knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture.Comment: Submitted for publication in CMAM

Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity

A new construction of biorthogonal splines for isogeometric mortar methods is proposed. The biorthogonal basis has a local support and, at the same time, optimal approximation properties, which yield optimal results with mortar methods. We first present the univariate construction, which has an inherent crosspoint modification. The multivariate construction is then based on a tensor product for weighted integrals, whereby the important properties are inherited from the univariate case. Numerical results including large deformations confirm the optimality of the newly constructed biorthogonal basis.Comment: biorthogonal basis, finite deformation, isogeometric analysis, mortar methods, multi-patch geometrie

Special Topics in Information Technology

This open access book presents thirteen outstanding doctoral dissertations in Information Technology from the Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy. Information Technology has always been highly interdisciplinary, as many aspects have to be considered in IT systems. The doctoral studies program in IT at Politecnico di Milano emphasizes this interdisciplinary nature, which is becoming more and more important in recent technological advances, in collaborative projects, and in the education of young researchers. Accordingly, the focus of advanced research is on pursuing a rigorous approach to specific research topics starting from a broad background in various areas of Information Technology, especially Computer Science and Engineering, Electronics, Systems and Control, and Telecommunications. Each year, more than 50 PhDs graduate from the program. This book gathers the outcomes of the thirteen best theses defended in 2019-20 and selected for the IT PhD Award. Each of the authors provides a chapter summarizing his/her findings, including an introduction, description of methods, main achievements and future work on the topic. Hence, the book provides a cutting-edge overview of the latest research trends in Information Technology at Politecnico di Milano, presented in an easy-to-read format that will also appeal to non-specialists

Numerical investigation of bone adaptation to exercise and fracture in Thoroughbred racehorses

Third metacarpal bone (MC3) fracture has a massive welfare and economic impact on horse racing, representing 45% of all fatal lower limb fractures, which in themselves represent more than 80% of reasons for death or euthanasia on the UK racecourses. Most of these fractures occur due to the accumulation of tissue fatigue as a result of repetitive loading rather than a specific traumatic event. Despite considerable research in the field, including applying various diagnostic methods, it still remains a challenge to accurately predict the fracture risk and prevent this type of injury. The objective of this thesis is to develop computational tools to quantify bone adaptation and resistance to fracture, thereby providing the basis for a viable and robust solution. Recent advances in subject-specific finite element model generation, for example computed tomography imaging and efficient segmentation algorithms, have significantly improved the accuracy of finite element modelling. Numerical analysis techniques are widely used to enhance understanding of fracture in bones and provide better insight into relationships between load transfer and bone morphology. This thesis proposes a finite element based framework allowing for integrated simulation of bone remodelling under specific loading conditions, followed by the evaluation of its fracture resistance. Accurate representation of bone geometry and heterogeneous material properties are obtained from calibrated computed tomography scans.The material mapping between CT-scan data and discretised geometries for the finite element method is carried out by using Moving Least Squares approximation and L2-projection. Thus is then used for numerical investigations and assessment of density gradients at the common site of fracture. Bone is able to adapt its density to changes in external conditions. This property is one of the most important mechanisms for the development of resistance to fracture. Therefore, a finite element approach for simulating adaptive bone changes (also called bone remodelling) is proposed. The implemented method is based on a phenomenological model of the macroscopic behaviour of bone based on the thermodynamics of open systems. Numerical results showed that the proposed technique has the potential to accurately simulate the long-term bone response to specified training conditions and also improve possible treatment options for bone implants. Assessment of the fracture risk was conducted with crack propagation analysis. The potential of two different approaches was investigated: smeared phase-field and discrete configurational mechanics approach. The popular phase-field method represents a crack by a smooth damage variable leading to a phase-field approximation of the variational formulation for brittle fracture. A robust solution scheme was implemented using a monolithic solution scheme with arc-length control. In the configurational mechanics approach, the driving forces, and fracture energy release rate, are expressed in terms of nodal quantities, enabling a fully implicit formulation for modelling the evolving crack front. The approach was extended for the first time to capture the influence of heterogeneous density distribution. The outcomes of this study showed that discrete and smeared crack approximations are capable of predicting crack paths in three-dimensional heterogeneous bodies with comparable results. However, due to the necessity of using significantly finer meshes, phase-field was found to be less numerically efficient. Finally, the current state of the framework's development was assessed using numerical simulations for bone adaptation and subsequent fracture propagation, including analysis of an equine metacarpal bone. Numerical convergence was demonstrated for all examples, and the use of singularity elements proved to further improve the rate of convergence. It was shown that bone adaptation history and bone density distribution influence both fracture resistance and the resulting crack path. The promising results of this study offer a~novel framework to simulate changes in the bone structure in response to exercise and quantify the likelihood of a fracture

Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics

The second MFO Oberwolfach Workshop on Mixed-Integer Nonlinear Programming (MINLP) took place between 2nd and 8th June 2019. MINLP refers to one of the hardest Mathematical Programming (MP) problem classes, involving both nonlinear functions as well as continuous and integer decision variables. MP is a formal language for describing optimization problems, and is traditionally part of Operations Research (OR), which is itself at the intersection of mathematics, computer science, engineering and econometrics. The scientific program has covered the three announced areas (hierarchies of approximation, mixed-integer nonlinear optimal control, and dealing with uncertainties) with a variety of tutorials, talks, short research announcements, and a special "open problems'' session