Computational synthesis of large deformation compliant mechanisms undergoing self and mutual contact

Topologies of large deformation Contact-aided Compliant Mechanisms (CCMs), with self and mutual contact, exemplified via path generation applications, are designed using the continuum synthesis approach. Design domains are parameterized using honeycomb tessellation. Assignment of material to each cell, and generation of rigid contact surfaces, are accomplished via suitably sizing and positioning negative circular masks. To facilitate contact analysis, boundary smoothing is implemented. Mean value coordinates are employed to compute shape functions, as many regular hexagonal cells get degenerated into irregular, concave polygons as a consequence of boundary smoothing. Both, geometric and material nonlinearities are considered in the finite element analysis. The augmented Lagrange multiplier method in association with an active set strategy is employed to incorporate both self and mutual contact. CCMs are evolved using the stochastic hill climber search. Synthesized contact-aided compliant continua trace paths with single and importantly, multiple kinks and experience multiple contact interactions pertaining to both self and mutual contact modes.Comment: 26 pages, 30 figures

On topology optimization of large deformation contact-aided shape morphing compliant mechanisms

A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal elements. Negative circular masks are employed to perform dual work, i.e., to decide material states of each element and also, to generate rigid contact surfaces. Each mask is characterized by five design variables, which are mutated by a zero-order based hill-climber optimizer. Geometric and material nonlinearities are considered. Continuity in normals to boundaries of the candidate designs is ensured using a boundary resolution and smoothing scheme. The nonlinear mechanical equilibrium equations are solved using the Newton-Raphson method. An updated Lagrange approach in association with segment-to-segment contact method is employed for the contact formulation. Both mutual and self contact modes are permitted. Efficacy of the approach is demonstrated by designing three contact-aided shape morphing compliant mechanisms for different desired curves. The performance of the deformed profiles is verified using a commercial software. The effect of frictional contact surface on the actual profile is also studied.Comment: 16 pages, 11 figure

Topological synthesis of fluidic pressure-actuated robust compliant mechanisms

This paper presents a robust density-based topology optimization approach for synthesizing pressure-actuated compliant mechanisms. To ensure functionality under manufacturing inaccuracies, the robust or three-field formulation is employed, involving dilated, intermediate and eroded realizations of the design. Darcy's law in conjunction with a conceptualized drainage term is used to model the pressure load as a function of the design vector. The consistent nodal loads are evaluated from the obtained pressure field using the standard finite element method. The objective and load sensitivities are obtained using the adjoint-variable approach. A multi-criteria objective involving both the stiffness and flexibility of the mechanism is employed in the robust formulation, and min-max optimization problems are solved to obtain pressure-actuated inverter, gripper, and contractor compliant mechanisms with different minimum feature sizes. Limitations of the linear elasticity assumptions while designing mechanisms are identified with high pressure loads. Challenges involved in designing finite deformable pressure-actuated compliant mechanisms are presented.Comment: 24 Figure

A Material Mask Overlay Strategy for Close to Binary Design-dependent Pressure-loaded Optimized Topologies

This paper presents a Material Mask Overlay Strategy topology optimization approach with improved material assignment at the element level for achieving close to black-and-white designs for pressure-loaded problems. Hexagonal elements are employed to parametrize the design domain as this tessellation provides nonsingular local connectivity. Elliptical negative masks are used to find the optimized material layout. The material dilation and material erosion variables of each mask are systematically varied in association with a gray-scale measure constraint to achieve designs close to 0-1. Darcy's law in association with a drainage term is used to formulate the pressure field. The obtained pressure field is converted into the consistent nodal forces using Wachspress shape functions. Sensitivities of the objective and pressure load are evaluated using the adjoint-variable method. The approach is demonstrated by solving various pressure-loaded structures and pressure-actuated compliant mechanisms. Compliance is minimized for loadbearing structures, whereas a multicriteria objective is minimized for mechanism designs.Comment: 22 pages, 16 figure

Topology Optimization and 3D printing of Large Deformation Compliant Mechanisms for Straining Biological Tissues

This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical nonlinearity together with a suitably chosen hypereleastic material model, wherein the mechanical equilibrium equations are solved using the total Lagrangian finite element formulation. An objective based on least-square error with respect to target strains is formulated and minimized with the given set of constraints and the appropriate surroundings of the tissues. To circumvent numerical instabilities arising due to large deformation in low stiffness design regions during topology optimization, a strain-energy based interpolation scheme is employed. The approach uses an extended robust formulation i.e. the eroded, intermediate and dilated projections for the design description as well as variation in tissue stiffness. Efficacy of the synthesis approach is demonstrated by designing various compliant mechanisms for providing different target strains in biological tissue constructs. Optimized compliant mechanisms are 3D-printed and their performances are recorded in a simplified experiment and compared with simulation results obtained by a commercial software.Comment: 23 pages, 14 figure

Internal contact modeling for finite strain topology optimization

The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact medium, makes the method suitable for cases with very large deformations. The proposed contact method is implemented in a second order topology optimization framework, which employs a coupled simultaneous solution of the mechanical, design update, and adjoint problems. All three problems are derived and presented in weak form, and discretized with finite elements of suitable order. The capabilities and accuracy of the developed method are demonstrated in a topology optimization problem for achieving a desired non-linear force-displacement path

Optimal Design of Beam-Based Compliant Mechanisms via Integrated Modeling Frameworks

Beam-based Compliant Mechanisms (CMs) are increasingly studied and implemented in precision engineering due to their advantages over the classic rigid-body mechanisms, such as scalability and reduced need for maintenance. Straight beams with uniform cross section are the basic modules in several concepts, and can be analyzed with a large variety of techniques, such as Euler-Bernoulli beam theory, Pseudo-Rigid Body (PRB) method, chain algorithms (e.g.~the Chained Beam-Constraint Model, CBCM) and Finite Element Analysis (FEA). This variety is unquestionably reduced for problems involving special geometries, such as curved or spline beams, variable section beams, nontrivial shapes and, eventually, contacts between bodies. 3D FEA (solid elements) can provide excellent results but the solutions require high computational times. This work compares the characteristics of modern and computationally efficient modeling techniques (1D FEA, PRB method and CBCM), focusing on their applicability in nonstandard problems. In parallel, as an attempt to provide an easy-to-use environment for CM analysis and design, a multi-purpose tool comprising Matlab and modern Computer-Aided Design/Engineering (CAD/CAE) packages is presented. The framework can implement different solvers depending on the adopted behavioral models. Summary tables are reported to guide the designers in the selection of the most appropriate technique and software architecture. The second part of this work reports demonstrative case studies involving either complex shapes of the flexible members or contacts between the members. To improve the clarity, each example has been accurately defined so as to present a specific set of features, which leads in the choice of a technique rather than others. When available, theoretical models are provided for supporting the design studies, which are solved using optimization approaches. Software implementations are discussed throughout the thesis. Starting from previous works found in the literature, this research introduces novel concepts in the fields of constant force CMs and statically balanced CMs. Finally, it provides a first formulation for modeling mutual contacts with the CBCM. For validation purposes, the majority of the computed behaviors are compared with experimental data, obtained from purposely designed test rigs

Topology optimization of compliant mechanisms based on the BESO method

This dissertation explores topology optimization techniques for designing compliant mechanisms actuated by forces. For a compliant mechanism, it has the potential of reducing part count, mechanical joints, operation noise, and manufacturing and assembly costs over a traditional rigid-link mechanism. Thus the application of compliant mechanisms is becoming increasingly prevalent in medical instruments and mechanical devices. Optimization of compliant mechanisms has drawn intense attention of many researchers. However, this design field has been facing many challenges and shortages in several aspects such as optimization method, optimization algorithm and resulting topology. For example, convergence problems often lead to vague solutions. Optimization algorithms are not very suitable to investigate the real physical significance. Furthermore, designs of compliant mechanisms using topology optimization techniques naturally lead to the introduction of hinges into final topologies. In addition, the previous design also focuses mainly on the optimal design of linear compliant mechanisms. In fact, optimizing nonlinear compliant mechanisms is proving quite necessary in real applications as the simulation is more accurate. Therefore, it is important to devote efforts to the modification of previous optimization techniques for constructing practical compliant mechanism designs. This dissertation proposes a modified bi-directional evolutionary structural optimization (BESO) method for the optimal design of linear and geometrically nonlinear compliant mechanisms. Numerical algorithms based on the BESO method are developed through various objectives and constraints in compliant mechanism design. Firstly, to consider functional behaviours of compliant mechanisms, sets of clear and suitable structural configurations are produced by quantifying various performance characteristics and changing the stiffness of attached springs. This implies that material distribution and hinge formation are demonstrated in this work. To achieve prescribed structural stiffness for optimized mechanisms, a new BESO algorithm is established for solving the proposed optimization problem by gradually updating design variables. The inverter and the gripper optimization problems serve to demonstrate the practicability and effectiveness of the proposed method. Besides this, a new formulation is established by considering desirable deformation and simultaneously precluding the formation of hinges in order to design hinge-free compliant mechanisms, verified by a large number of numerical experiments including rare 3D hinge-free designs. Furthermore, compliant mechanisms often undergo large displacement, in order to provide their functionality. Therefore, the research also addresses the optimal design of compliant mechanism with geometrically nonlinear behaviours. With the aid of the hard-kill BESO method, a new systemic design approach is developed to overcome the convergence difficulty caused by extreme deformation in the nonlinear finite element analysis. Large-displacement inverter design with the desired structural stiffness is provided based on a new evolutionary optimization technique involved in a developed multi-criteria flexibility-stiffness formulation. Overall, the modified BESO method has effectively set up new optimizations, visualizing and analysing the resulting topologies for 2D and 3D compliant mechanism designs. The findings shown in this dissertation have also established appropriate techniques for designing various linear compliant mechanisms. In addition, an efficient and robust methodology has been provided for the topology optimization of geometrically nonlinear compliant mechanisms. Furthermore, the work has provided a solid foundation for creating a practical design tool in the form of a user-friendly computer program, which is suitable for the conceptual design of a wide range of compliant mechanisms

Applied Analysis and Synthesis of Complex Systems: Proceedings of the IIASA-Kyoto University Joint Seminar, June 28-29, 2004

This two-day seminar aimed at introducing the new development of the COE by Kyoto University to IIASA and discussing general modeling methodologies for complex systems consisting of many elements, mostly via nonlinear, large-scale interactions. We aimed at clarifying fundamental principles in complex phenomena as well as utilizing and synthesizing the knowledge derived out of them. The 21st Century COE (Center of Excellence) Program is an initiative by the Japanese Ministry of Education, Culture, Science and Technology (MEXT) to support universities establishing discipline-specific international centers for education and research, and to enhance the universities to be the world's apex of excellence with international competitiveness in the specific research areas. Our program of "Research and Education on Complex Functional Mechanical Systems" is successfully selected to be awarded the fund for carrying out new research and education as Centers of Excellence in the field of mechanical engineering in 2003 (five-year project), and is expected to lead Japanese research and education, and endeavor to be the top in the world. The program covers general backgrounds in diverse fields as well as a more in-depth grasp of specific branches such as complex system modeling and analysis of the problems including: nonlinear dynamics, micro-mesoscopic physics, turbulent transport phenomena, atmosphere-ocean systems, robots, human-system interactions, and behaviors of nano-composites and biomaterials. Fundamentals of those complex functional mechanical systems are macroscopic phenomena of complex systems consisting of microscopic elements, mostly via nonlinear, large-scale interactions, which typically present collective behavior such as self-organization, pattern formation, etc. Such phenomena can be observed or created in every aspect of modern technologies. Especially, we are focusing upon; turbulent transport phenomena in climate modeling, dynamical and chaotic behaviors in control systems and human-machine systems, and behaviors of mechanical materials with complex structures. As a partial attainment of this program, IIASA and Kyoto University have exchanged Consortia Agreement at the beginning of the program in 2003, and this seminar was held to introduce the outline of the COE program of Kyoto University to IIASA researchers and to deepen the shared understandings on novel complex system modeling and analysis, including novel climate modeling and carbonic cycle management, through joint academic activities by mechanical engineers and system engineers. In this seminar, we invited a distinguished researcher in Europe as a keynote speaker and our works attained so far in the project were be presented by the core members of the project as well as by the other contributing members who participated in the project. All IIASA research staff and participants of YSSP (Young Scientist Summer Program) were cordially invited to attend this seminar to discuss general modeling methodologies for complex systems