Rubén Ansola

An integrated approach for shape and topology optimization of shell structures

In this paper an automated approach for simultaneous shape and topology optimization of shell structures is presented. Most research in the last decades considered these optimization techniques separately, seeking an initial optimal material layout and refining the shape of the solution later. The method developed in this work combines both optimization techniques, where the shape of the shell structure and material distribution are optimized simultaneously, with the aim of finding the optimum design that maximizes the stiffness of the shell. This formulation involves a variable ground structure for topology optimization, since the shape of the shell is modified in the course of the process. The method has been implemented into a computational model and the feasibility of the approach is demonstrated using several examples.

Dental implants with conical implant-abutment interface: influence of the conical angle difference on the mechanical behavior of the implant.

PURPOSE Misfit in the conical implant-abutment interface plays an important role on the mechanical behavior of the implant when masticatory forces are applied. The origin of the misfit adopted in this work is a conical angle difference between implant and abutment, which can be due to a combination of design decisions and manufacturing tolerances. The goal of this work was to investigate the effects of the implant-abutment conical angle difference in the following mechanical features: interfacial microgap, preload loss on the bolt, stress level in the bone, and abutment removal force and/or torque. MATERIALS AND METHODS A simplified three-dimensional nonlinear monoparametric finite element model of an OsseoSpeed TX 4.5 S 9-mm implant (Astra Tech) with a tapered implant-abutment interface was built to evaluate the variability of the mechanical features cited above with the conical angle difference, keeping constant the overall geometry, load and boundary conditions, material properties, frictional behavior, and mesh structure. RESULTS As the conical angle difference increased, the following effects were observed: the microgap decreased and remained almost constant for values over a given positive angle difference, the stress level in the bone increased sensitively, the removal force and/or torque needed to separate the abutment from the implant varied slightly, and the bolt preload loss increased. CONCLUSIONS In light of the results provided, the conical angle difference in the implant-abutment interface had a significant influence on the overall mechanical behavior of the implant. Among the four mechanical features considered, the interfacial microgap and the bone stress were demonstrated to be the most sensitive to the conical angle difference, and therefore the most relevant when selecting an optimum value in the design process of a conical interface.

An element addition strategy for thermally actuated compliant mechanism topology optimization

Purpose – The purpose of this paper is to describe an element addition strategy for topology optimization of thermally actuated compliant mechanisms under uniform temperature fields.Design/methodology/approach – The proposed procedure is based on the evolutionary structural optimization (ESO) method. In previous works, this group of authors has successfully applied the ESO method for compliant mechanism optimization under directly applied input loads. The present paper progresses on this work line developing an extension of this procedure, based on an additive version of the method, to approach the more complicated case of thermal actuators.Findings – The adopted method has been tested in several numerical applications and benchmark examples to illustrate and validate the approach, and designs obtained with this method are compared favorably with the analytical solutions and results derived by other authors using different optimization methods, showing the viability of this technique for uniformly heated ...

An alternative full-pivoting algorithm for the factorization of indefinite symmetric matrices

This paper presents an algorithm for the factorization of indefinite symmetric matrices that factors any symmetric matrix A into the form LDL^T, with D diagonal and L triangular, with its subdiagonal filled with zeros. The algorithm is based on Jacobi rotations, as opposed to the widely used permutation methods (Aasen, Bunch-Parlett, and Bunch-Kaufman). The method introduces little increase in computational cost and provides a bound on the elements of the reduced matrices of order 2nf(n), which is smaller than that of the Bunch-Parlett method (~3nf(n)), and similar to that of Gaussian elimination with full pivoting (nf(n)). Furthermore, the factorization method is not blocked. Although the method presented is formulated in a full-pivoting scheme, it can easily be adapted to a scheme similar to that of the Bunch-Kaufman approach. A backward error analysis is also presented, showing that the elements of the error matrix can be bounded in terms of the elements of the reduced matrices.

Topology synthesis of Multi-Input–Multi-Output compliant mechanisms

Abstract A generalized formulation to design Multi-Input–Multi-Output (MIMO) compliant mechanisms is presented in this work. This formulation also covers the simplified cases of the design of Multi-Input and Multi-Output compliant mechanisms, more commonly used in the literature. A Sequential Element Rejection and Admission (SERA) method is used to obtain the optimum design that converts one or more input works into one or more output displacements in predefined directions. The SERA procedure allows material to flow between two different material models: ‘real’ and ‘virtual’. The method works with two separate criteria for the rejection and admission of elements to efficiently achieve the optimum design. Examples of Multi-Input, Multi-Output and MIMO compliant mechanisms are presented to demonstrate the validity of the proposed procedure to design complex complaint mechanisms.

Parameter study of a SERA method to design compliant mechanism

A Sequential Element Rejection and Admission (SERA) method is used in this work to design compliant mechanisms. This discrete method allows material to flow between two different material models: ‘real’ and ‘virtual’. It is bi-directional in nature and works with two separate criteria for the rejection and admission of elements to efficiently achieve the optimum design. The aim of this paper is to study the robustness and versatility of the SERA method for compliant mechanisms design by means of a study of the main problem parameters (mesh density, target volume fraction, input and output stiffness, initial design domain, and filtering radius). Also, as part of the study of different initial design domains, an explanation is given on why the additional version of the ESO method is needed to design compliant mechanisms when an unidirectional approach is considered.

Electro-thermal compliant mechanisms design by an evolutionary topology optimization method

Purpose – This paper aims to show an evolutionary topology optimization procedure for the design of compliant electro-thermal mechanisms. Design/methodology/approach – The adopted methodology is based in the evolutionary structural optimization (ESO) method. This approach has been successfully applied by this group for compliant mechanisms optimization under directly applied input loads and simple thermal loads. This work proposes an extension of this procedure, based on an additive version of the method, to solve the more complicated case of electro-thermal actuators optimum design, based on Joules resistive heating. Findings – Examples solved for the design of plane compliant mechanisms are presented to check the validity of this technique. The designs obtained are compared favorably with results obtained by other authors to illustrate and validate the method, showing the viability of this technique for the optimization of compliant mechanisms under electro-thermal actuation. Research limitations/impli...

A Flexible Overhang Constraint for Topology Optimization of Compliant Mechanisms. Advantages of Controlling the Additive Manufacturability/Performance Ratio

The concept “Topology Optimization for Additive Manufacturing” is a recently coined concept that refers to the complete engagement of topology optimization problems and additive manufacturing processes. The idea of coupling both technologies through a specific overhang constraint lies in the idea of a total design freedom, which classic manufacturing processes are unable to reach. If any design can be build, this will enable a continuum “design + manufacturing” process eliminating prost-processing and any interference with the optimized geometry. In the field of structures there are already some ground-breaking approaches, there aren’t however any regarding the optimization of compliant mechanisms. The introduction of the overhang constraint within the topology optimization formulation of compliant mechanisms yields a compromise or inverse relation of functionality and manufacturability. The hinges of the flexible mechanisms are formed by a sharp thinning of the material members and describe a shape that possesses many tangents with different slopes, some of them showing not self supported contours. There is an inverse relation there for functionality and manufacturability. If the hinge is to be corrected so that a direct 3D printing of the mechanisms is possible, the global objective function will be harmed as the optimum-functional shape of the hinge is set aside. This paper introduces the advantages of a flexible overhang constraint for a more accurate topology optimization of 3D printed compliant mechanisms enabling intermediate design for different manufacturability/functionality ratios, and analyses the consequences of fully restricting scaffold structures respect to controlling and reducing them.

Topology Optimization as a Digital Design Tool

Topology optimization has emerged as a powerful and useful tool for the design of structures, a contributing factor being the emergence of computational speed and power. The design process has also been affected by computers which have changed the concept of form into the concept of formation and the emergence of digital design. Topology optimization can modify existing designs, incorporate explicit features into a design, and generate completely new designs; however, this has mostly only been appreciated by structural designers and engineers, and not by the wider field of product design. This chapter shows how topology optimization can be used as a digital tool by investigating several examples.

Continuous Method of Structural Optimization

This chapter presents the Isolines/Isosurfaces Topology Design (ITD) method which allows for the continuous optimization of the topology of a structure. For a two-dimensional (2D) domain, ITD uses the isolines, and for a three-dimensional (3D) domain, it uses the isosurfaces of the response used for the optimization of the structure. The topology and hence shape of the design, depends on an iterative process which continually adds and removes material. The material admission and removal process uses the shape and distribution of the contour isolines/isosurfaces of the required structural behaviour.