Topology optimization of structures considering minimum weight and stress constraints by using the Overweight Approach

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract:] In this paper, a new method for structural topology optimization considering minimum weight and local stress constraints is proposed. For this purpose, the Overweight Approach, an improvement of the so-called Damage Approach, is used. In this method, a virtual relative density is defined as a function of the violation of the local stress constraints. The virtual relative density is increased as stresses exceed the maximum allowable value. The optimization algorithm will provide a design with a minimal variation of the relative density. The structural analysis is performed by means of the Finite Element Method (FEM) and the distribution of material is modelled in terms of a uniform relative density within each element. Moreover, the optimization is addressed by means of the Sequential Linear Programming algorithm (SLP). Finally, the proposed methodology is tested by means of some benchmark problems, and the results show that the Overweight Approach is a feasible alternative for the Damage Approach and the stress constraint aggregation techniques.Xunta de Galicia; ED481A-2016/387Xunta de Galicia; GRC2014/039Xunta de Galicia; GRC2018/41This work has been partially supported by the “Xunta de Galicia, Spain (Secretaría Xeral de Universidades)” and the European Union (European Social Fund - ESF) through “Grants for supporting the predoctoral stage in universities of the Galician University System, in research public organisms of Galicia and in other entities of the “R & D system of the Galician Government - 2016” ED481A-2016/387, by Feder funds of the European Union, by the “Ministerio de Economía y Competitividad, Spain” of the Spanish Government through grants DPI2015-68431-R and RTI2018-093366-B-I00, by the “Consellería de Educación, Universidade e Formación Profesional, Spain” of the “Xunta de Galicia” through “grants for the consolidation and structuring of competitive research units of the Galician University System: Competitive reference group” GRC2014/039 and GRC2018/41, and by research fellowships of the University of A Coruña, Spain and the “Fundación de la Ingeniería Civil de Galicia, Spain ”

Computational Evolutionary Embryogeny

Evolutionary and developmental processes are used to evolve the configurations of 3-D structures in silico to achieve desired performances. Natural systems utilize the combination of both evolution and development processes to produce remarkable performance and diversity. However, this approach has not yet been applied extensively to the design of continuous 3-D load-supporting structures. Beginning with a single artificial cell containing information analogous to a DNA sequence, a structure is grown according to the rules encoded in the sequence. Each artificial cell in the structure contains the same sequence of growth and development rules, and each artificial cell is an element in a finite element mesh representing the structure of the mature individual. Rule sequences are evolved over many generations through selection and survival of individuals in a population. Modularity and symmetry are visible in nearly every natural and engineered structure. An understanding of the evolution and expression of symmetry and modularity is emerging from recent biological research. Initial evidence of these attributes is present in the phenotypes that are developed from the artificial evolution, although neither characteristic is imposed nor selected-for directly. The computational evolutionary development approach presented here shows promise for synthesizing novel configurations of high-performance systems. The approach may advance the system design to a new paradigm, where current design strategies have difficulty producing useful solutions

Topology Optimization of Structures with High Spatial Definition Considering Minimum Weight and Stress Constraints

Programa Oficial de Doutoramento en Enxeñaría Civil . 5011V01[Abstract] The first formulation of Topology Optimization was proposed in 1988. Since then, many contributions have been presented with the purpose of improving its efficiency and extending its applicability. In this thesis, a topology optimization algorithm that allows to obtain the structure of minimum weight that is able to support different loads is developed. For this purpose, the requirement that stresses have to be lower than a maximum value has been considered in its development. Although the structural topology optimization problem with stress constraints have been previously formulated with several different approaches, a Damage Constraint approach is developed in this thesis to incorporate them in a different way. The main objective of this modification is to reduce the CPU time required in the solution of the topology optimization problem. This reduction will allow to solve problems with a higher number of design variables what enables the attainment of solutions with high spatial definition. Moreover, two different approaches are used to define the material distribution in the domain: uniform density per element formulation and material density distribution by means of isogeometric interpolation. In the first approach the Finite Element Method (FEM) is used to solve the structural analysis and the relative density in each element of the mesh is chosen as design variable, while the second one uses the Isogeometric Analysis (IGA) for solving the structural analysis and the values of the relative density at a certain number of control points are used as design variables. On the other hand, the optimization is addressed by using Sequential Linear Programming, that requires a first order sensitivity analysis. All the sensitivities are obtained through analytic derivatives by using both, direct differentiation and the adjoint variable method. Finally, some application examples are solved by means of both methods (FEM and IGA) in the two-dimensional and three-dimensional space.[Resumen] La primera formulación de la Optimización Topológica fue propuesta en 1988. Desde entonces muchas aportaciones se han presentado para mejorar su eficiencia y extender su aplicabilidad. En esta tesis se desarrolla un algoritmo de optimización topológica que permita obtener la estructura de mínimo peso que sea capaz de soportar diferentes cargas. Para este propósito se ha considerado en su desarrollo la condición de que las tensiones sean inferiores a un cierto valor máximo. Aunque el problema de optimización topológica estructural con restricciones de tensión se formuló previamente con diferentes enfoques, en esta tesis se desarrolla un enfoque que considera una restricción de daño para incorporarlas de una forma diferente. El principal objetivo de esta modificación es reducir el tiempo de computación requerido en la solución del problema de optimización topológica. Esta reducción permitir ´a resolver problemas con un mayor número de variables de diseño lo que a su vez permite la obtención de soluciones con alta definición espacial. Para definir la distribución de material en el dominio se usan dos formulaciones diferentes: formulación de densidad uniforme por elemento y distribución de material por medio de una interpolación isogeométrica. El primer planteamiento usa el Método de los Elementos Finitos (MEF) para resolver el análisis estructural y toma como variable de diseño el valor de la densidad relativa en cada elemento de la malla, mientras que el segundo requiere del uso del Análisis Isogeométrico (IGA) para resolver el análisis estructural y los valores de la densidad relativa en un cierto número de puntos de control son las variables de diseño. El problema de optimización se resuelve con las técnicas de Programación Lineal Secuencial requiriendo ´únicamente el análisis de sensibilidad de primer orden. Todas las derivadas se calculan por derivación analítica haciendo uso de las técnicas de derivación directa y del método de la variable adjunta. Finalmente, se resuelven algunos ejemplos de aplicación con ambos métodos (MEF e IGA) en el espacio bidimensional y tridimensional.[Resumo] A primeira formulación da Optimización Topolóxica foi proposta en 1988. Desde entón moitas achegas se presentaron para mellorar a súa eficiencia e estender a súa aplicabilidade. Nesta tese desenvólvese un algoritmo de optimización topolóxica que permita obter a estrutura de mínimo peso que sexa capaz de soportar diferentes cargas. Para este propósito considerouse no seu desenvolvemento a condición de que as tensións sexan inferiores a un certo valor máximo. Aínda que o problema de optimización topolóxica estrutural con restricións de tensi´on formulouse previamente con diferentes enfoques, nesta tese desenvólvese un enfoque que considera unha restrición de dano para incorporalas dunha forma diferente. O principal obxectivo desta modificación é reducir o tempo de computación requirido na solución do problema de optimizaci´on topol´oxica. Esta reduci´on permitir´a resolver problemas cun maior número de variables de dese˜no o que ´a s´ua vez permite a obtención de solucións con alta definición espacial. Para definir a distribución de material no dominio úsanse dúas formulacións diferentes: formulación de densidade uniforme por elemento e distribución de material por medio dunha interpolación isoxeométrica. A primeira formulación usa o Método dos Elementos Finitos (MEF) para resolver a análise estrutural e toma coma variable de deseño o valor da densidade relativa en cada elemento da malla, mentres que o segundo require do uso da Análise Isoxeométrica (IGA) para resolver a análise estrutural e os valores da densidade relativa nun certo número de puntos de control son as variables de deseño. O problema de optimización resólvese coas técnicas de Programación Lineal Secuencial requirindo unicamente a análise de sensibilidade de primeira orde. Todas as derivadas calcúlanse por derivación analítica facendo uso das técnicas de derivación directa e do método da variable adxunta. Finalmente, resólvense algúns exemplos de aplicación con ámbolos métodos (MEF e IGA) no espazo bidimensional e tridimensionalMinisterio de Economía y Competitividad; DPI2015-68341-RMinisterio de Economía y Competitividad; RTI2018-093366-B-I00Xunta de Galicia; GRC2014/039Xunta de Galicia; GRC2018/4

Passive Aeroelastic Tailoring

The Passive Aeroelastic Tailoring (PAT) project was tasked with investigating novel methods to achieve passive aeroelastic tailoring on high aspect ratio wings. The goal of the project was to identify structural designs or topologies that can improve performance and/or reduce structural weight for high-aspect ratio wings. This project considered two unique approaches, which were pursued in parallel: through-thickness topology optimization and composite tow-steering

Topology Optimization Method for Dynamic Fatigue Constraints Problem

In this research, a new topology optimization (TO) method was proposed to consider dynamic failure criteria (fatigue) under constant and proportional loading. Despite the great development of the topology optimization, the TO method considering the static or dynamic failure constraints has been regarded as one of the difficult problems. Although the TO method for the static failure has been studied extensively nowadays, the TO method considering the dynamic fatigue constraints is remained as an unexplored field. In order to address the dynamic failure in TO, this research develops a new fatigue-constrained topology optimization procedure. Because the dynamic responses as well as the static responses should be considered, it is more difficult than the stress-based topology optimization due to the non-differentiable fatigue criteria of the modified Goodman, the Soderberg and the Gerber theories. By addressing these issues numerically, this research can solve the topology optimization problem considering the fatigue constraint successfully.This work was supported by the 2012 Second Brain Korea 21 Project. Also, this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.2012-0005530)