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Symbolic computation in applied computational mechanics
Journal of Symbolic Computation 61–62 (2014) 1–2
Contents lists available at ScienceDirect
Journal of Symbolic Computation www.elsevier.com/locate/jsc
Foreword
Symbolic computation in applied computational mechanics This Special Issue of the Journal of Symbolic Computation contains the edited version of some selected papers presented at CSEI2012 – National Conference on Symbolic Computation in Education and Research that was held on April 2–3, 2012, in IST – Instituto Superior Técnico, Technical University of Lisbon, Portugal. The conference was organized by IDMEC/IST, under the auspice of the APMTAC – Associação Portuguesa de Mecânica Teórica Aplicada e Computacional (Portuguese Society of Theoretical, Applied and Computational Mechanics). The Portuguese Society of Theoretical, Applied and Computational Mechanics is the natural evolution from the CPMTA – Comissão Portuguesa de Mecânica Teórica e Aplicada (Portuguese Commission for Theoretical and Applied Mechanics) that it is affiliated to IACM, ECCOMAS and IUTAM since 1973 and it is coordinated by Prof. Carlos Mota Soares. This Special Issue deals with the application of symbolic computation in applied computational mechanics. It contains 4 papers of greater relevance in this topic, presented at the CSEI2012 Conference, after acceptance by the referees for publication. The main problems addressed in this Issue are the automation and systematization of complex mechanical problems enabling significant time savings, the advantages of merging numerical and symbolic facets of the problems solving process, the development of hybrid analytical-experimental techniques and the generation of toolpaths for additive layered fabrication. The symbolic computation platforms emerged in recent decades as a tool, combining mathematics and computer science, allowing achieving analytical responses for various problems involving algebraic calculation, using object-oriented programming. The main advantages of using symbolic manipulators can be summarized in four aspects: substantial reduction of time consumption in tedious manual calculations, increased computational efficiency and numerical stability, substantial reduction in time needed to develop new theories or test new concepts, which often require many months of manual effort and easy connection of the numerical calculation, analytical and graphical. It is upon this background perspective that the papers for this Issue were selected. This Issue aims to show that the use of symbolic computation, allows not only the resolution of complex problems, but also represents a powerful tool for the understanding of concepts and links, unimaginable a few years ago, which in the applied mechanics context ranges from structural analysis to control theory. The existence of closed form solutions or the possibility to derive new ones by analytical means represents a strong motivation to use symbolic computation in applied computational mechanics. Next we summarize the main ideas presented in the papers of this issue: Symbolic and numerical analysis of plates in bending using Matlab, Roque, C.M.C. The first paper of this Issue deals with the application of the meshless method to solve the bending of composite plates, using a third order shear deformation theory. The symbolic manipulation of governing equations it was used to the implementation of the meshless collocation method using radial basis functions for solving partial differential equations, associated to the equilibrium equations of a composite plate in bending. The symbolic program developed takes a few seconds to run and a 0747-7171/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.jsc.2013.10.004
2
Foreword
few minutes for the programmer to adapt it to a new shear deformation theory. The technique can be applied to many shear deformation theories, for static and dynamic modeling of plates and shells. On the use of particle swarm optimization to maximize bending stiffness of functionally graded structures, Loja, M.A.R. In this paper it is studied the use of particle swarm optimization technique for the maximization of a functionally graded sandwich beam bending stiffness. A set of case studies is analyzed, in order to enable to understand in a detailed way, how different optimization parameters tuning, can influence the whole process. A re-initialization strategy it is also considered. The utilization of symbolic computation in the study of the maximization of a graded sandwich beam bending stiffness was considered as an approach to take also into account for minimizing transverse displacement or maximizing natural frequencies, in alternative to carrying out a significant number of finite element analyses, which would involve expensive computational costs. The studies carried out show a globally good performance of the particle swarm optimization technique. On a hybrid analytical-experimental technique to assess the storage modulus of resilient materials using symbolic computation, Policarpo, H., Neves, M.M. and Maia, N.M.M. The paper deals with the application of symbolic computation to develop hybrid analyticalexperimental methods using a simple example of solid mechanics, involving a boundary value problem with hyperbolic differential equation and Neumann boundary condition from the classical theory of longitudinal vibration of rods. This hybrid analytical-experimental technique, obtained using symbolic computation proved to be more rigorous than a finite element based solution and more rigorous than the discrete mass-spring model often used in this kind of experimental tests. The proposed methodology was validated for composition cork-like materials, although it may be applied to other linear viscoelastic materials. A procedure for computing the symmetric difference of regions defined by polygonal curves, Gaspar, M.B. and Martins-Ferreira, N. The paper provides a detailed description of a procedure to be used in calculating the symmetric difference for arbitrary regions in the plane. Since the whole process is more topological than geometrical, it can be used to calculate the symmetric difference of any two regions embedded in an oriented 2-manifold, while opening the way for a future study in higher dimensions. The algorithm presented has been developed for use in the context of generation of toolpaths for additive layered fabrication. In this application, a triangulated closed surface is decomposed in parallel horizontal slices, to be fabricated on top of each other, with each slice defined by its polygonal boundary. The Guest Editor deeply appreciated the effort of the authors in writing the lectures and the papers in time, allowing this Special Issue to be published as planned. We appreciate the strong leadership of the Editor-in-Chief of the Journal of Symbolic Computation, Prof. Hoon Hong, which made possible the publication of this Special Issue. We acknowledge the outstanding work of all reviewers, which allowed this Special Issue to be published.
Guest Editor Joaquim Infante Barbosa a,b a IDMEC/LAETA – Instituto de Engenharia Mecânica, Portugal b
ADEM/ISEL – Instituto Superior de Engenharia de Lisboa, Portugal E-mail address: [email protected] 7 August 2013 Available online 15 October 2013
Contents lists available at ScienceDirect
Journal of Symbolic Computation www.elsevier.com/locate/jsc
Foreword
Symbolic computation in applied computational mechanics This Special Issue of the Journal of Symbolic Computation contains the edited version of some selected papers presented at CSEI2012 – National Conference on Symbolic Computation in Education and Research that was held on April 2–3, 2012, in IST – Instituto Superior Técnico, Technical University of Lisbon, Portugal. The conference was organized by IDMEC/IST, under the auspice of the APMTAC – Associação Portuguesa de Mecânica Teórica Aplicada e Computacional (Portuguese Society of Theoretical, Applied and Computational Mechanics). The Portuguese Society of Theoretical, Applied and Computational Mechanics is the natural evolution from the CPMTA – Comissão Portuguesa de Mecânica Teórica e Aplicada (Portuguese Commission for Theoretical and Applied Mechanics) that it is affiliated to IACM, ECCOMAS and IUTAM since 1973 and it is coordinated by Prof. Carlos Mota Soares. This Special Issue deals with the application of symbolic computation in applied computational mechanics. It contains 4 papers of greater relevance in this topic, presented at the CSEI2012 Conference, after acceptance by the referees for publication. The main problems addressed in this Issue are the automation and systematization of complex mechanical problems enabling significant time savings, the advantages of merging numerical and symbolic facets of the problems solving process, the development of hybrid analytical-experimental techniques and the generation of toolpaths for additive layered fabrication. The symbolic computation platforms emerged in recent decades as a tool, combining mathematics and computer science, allowing achieving analytical responses for various problems involving algebraic calculation, using object-oriented programming. The main advantages of using symbolic manipulators can be summarized in four aspects: substantial reduction of time consumption in tedious manual calculations, increased computational efficiency and numerical stability, substantial reduction in time needed to develop new theories or test new concepts, which often require many months of manual effort and easy connection of the numerical calculation, analytical and graphical. It is upon this background perspective that the papers for this Issue were selected. This Issue aims to show that the use of symbolic computation, allows not only the resolution of complex problems, but also represents a powerful tool for the understanding of concepts and links, unimaginable a few years ago, which in the applied mechanics context ranges from structural analysis to control theory. The existence of closed form solutions or the possibility to derive new ones by analytical means represents a strong motivation to use symbolic computation in applied computational mechanics. Next we summarize the main ideas presented in the papers of this issue: Symbolic and numerical analysis of plates in bending using Matlab, Roque, C.M.C. The first paper of this Issue deals with the application of the meshless method to solve the bending of composite plates, using a third order shear deformation theory. The symbolic manipulation of governing equations it was used to the implementation of the meshless collocation method using radial basis functions for solving partial differential equations, associated to the equilibrium equations of a composite plate in bending. The symbolic program developed takes a few seconds to run and a 0747-7171/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.jsc.2013.10.004
2
Foreword
few minutes for the programmer to adapt it to a new shear deformation theory. The technique can be applied to many shear deformation theories, for static and dynamic modeling of plates and shells. On the use of particle swarm optimization to maximize bending stiffness of functionally graded structures, Loja, M.A.R. In this paper it is studied the use of particle swarm optimization technique for the maximization of a functionally graded sandwich beam bending stiffness. A set of case studies is analyzed, in order to enable to understand in a detailed way, how different optimization parameters tuning, can influence the whole process. A re-initialization strategy it is also considered. The utilization of symbolic computation in the study of the maximization of a graded sandwich beam bending stiffness was considered as an approach to take also into account for minimizing transverse displacement or maximizing natural frequencies, in alternative to carrying out a significant number of finite element analyses, which would involve expensive computational costs. The studies carried out show a globally good performance of the particle swarm optimization technique. On a hybrid analytical-experimental technique to assess the storage modulus of resilient materials using symbolic computation, Policarpo, H., Neves, M.M. and Maia, N.M.M. The paper deals with the application of symbolic computation to develop hybrid analyticalexperimental methods using a simple example of solid mechanics, involving a boundary value problem with hyperbolic differential equation and Neumann boundary condition from the classical theory of longitudinal vibration of rods. This hybrid analytical-experimental technique, obtained using symbolic computation proved to be more rigorous than a finite element based solution and more rigorous than the discrete mass-spring model often used in this kind of experimental tests. The proposed methodology was validated for composition cork-like materials, although it may be applied to other linear viscoelastic materials. A procedure for computing the symmetric difference of regions defined by polygonal curves, Gaspar, M.B. and Martins-Ferreira, N. The paper provides a detailed description of a procedure to be used in calculating the symmetric difference for arbitrary regions in the plane. Since the whole process is more topological than geometrical, it can be used to calculate the symmetric difference of any two regions embedded in an oriented 2-manifold, while opening the way for a future study in higher dimensions. The algorithm presented has been developed for use in the context of generation of toolpaths for additive layered fabrication. In this application, a triangulated closed surface is decomposed in parallel horizontal slices, to be fabricated on top of each other, with each slice defined by its polygonal boundary. The Guest Editor deeply appreciated the effort of the authors in writing the lectures and the papers in time, allowing this Special Issue to be published as planned. We appreciate the strong leadership of the Editor-in-Chief of the Journal of Symbolic Computation, Prof. Hoon Hong, which made possible the publication of this Special Issue. We acknowledge the outstanding work of all reviewers, which allowed this Special Issue to be published.
Guest Editor Joaquim Infante Barbosa a,b a IDMEC/LAETA – Instituto de Engenharia Mecânica, Portugal b
ADEM/ISEL – Instituto Superior de Engenharia de Lisboa, Portugal E-mail address: [email protected] 7 August 2013 Available online 15 October 2013