Topological Design of Multi-Material Compliant Mechanisms with Global Stress Constraints

This paper presents an approach for the topological design of multi-material compliant mechanisms with global stress constraints. The element stacking method and the separable stress interpolation scheme are applied to calculate the element stiffness and element stress of multi-material structures. The output displacement of multi-material compliant mechanisms is maximized under the constraints of the maximum stress and the structural volume of each material. The modified P-norm method is applied to aggregate the local von Mises stress constraints for all the finite elements to a global stress constraint. The sensitivities are calculated by the adjoint method, and the method of moving asymptotes is utilized to update the optimization problem. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. The appearance of the de facto hinges in the optimal mechanisms can be suppressed effectively by using the topology optimization model with global stress constraints, and the stress constraints for each material can be met.

Topology Optimization for Additively Manufactured Self-Supporting Axisymmetric Structures

This paper discusses the design of axisymmetric structures with self-supporting features that can be additively manufactured without requiring internal support structures. This is motivated by wire-fed additive manufacturing processes, many of which can fabricate designs with enclosed pores that inherently exist in many axisymmetric structures, such as double walled pressure vessels. Although enclosed pores are possible, features that rise at shallow angles from the build plate typically cannot be fabricated without the use of support structures, which require removal and thus are unfavorable in such applications. In this paper, an overhang constraint is applied to ensure that all designed features rise at a designer-prescribed self-supporting angle to eliminate the need for such support structures. This is achieved by coupling the projection-based overhang constraint approach with topology optimization and axisymmetric finite elements whose stiffness is interpolated using Solid Isotropic Material with Penalization (SIMP). Gradients are computed with the adjoint method and the Method of Moving Asymptotes (MMA) is employed as the gradient-based optimizer. Two numerical examples related to a canonical pressure vessel and an optical mirror support structure are used to demonstrate the approach. Solutions are shown to satisfy minimum feature size requirements and designer-prescribed (process dependent) overhang constraint angles, while providing clear and crisp representations of topology. As observed in past works on overhang constraints, a clear trade-off is illustrated between the magnitude of the overhang constraint angle and the structural performance (mass or stiffness), with more strict requirements producing designs with lower performance.

Optimal design of piezoelectric cantilever velocity sensor based on PVDF

The response charge of piezoelectric speed sensors using a conventional rectangular cantilever is low, which also causes a low sensitivity in speed measurement. To improve the sensor sensitivity, a piezoelectric speed sensor based on a streamlined piezoelectric cantilever is employed in this paper. Furthermore, a theoretical optimization model of the sensor based on Bernstein polynomial equation is established, and a simulation optimization flow work is also proposed. With method of moving asymptotes (MMA) algorithm, more charge output can be obtained than before. The simulation results show that the optimized sensor can output a voltage of 416 mV and obtain a sensitivity of 52 mV/m⋅s−1 when the input speed is 8 m/s. As compared with the values of 300 mV and 37.5 mV/m⋅s−1 in the un-optimized case, the improvement in the sensor sensitivity is up to 38%, which confirms the effectiveness of the proposed method.

Topology Optimization of Multi-Materials Compliant Mechanisms

In this article, a design method of multi-material compliant mechanism is studied. Material distribution with different elastic modulus is used to meet the rigid and flexible requirements of compliant mechanism at the same time. The solid isotropic material with penalization (SIMP) model is used to parameterize the design domain. The expressions for the stiffness matrix and equivalent elastic modulus under multi-material conditions are proposed. The least square error (LSE) between the deformed and target displacement of the control points is defined as the objective function, and the topology optimization design model of multi-material compliant mechanism is established. The oversaturation problem in the volume constraint is solved by pre-setting the priority of each material, and the globally convergent method of moving asymptotes (GCMMA) is used to solve the problem. Widely studied numerical examples are conducted, which demonstrate the effectiveness of the proposed method.

Generalized Optimality Criteria Method for Topology Optimization

In this article, a generalized optimality criteria method is proposed for topology optimization with arbitrary objective function and multiple inequality constraints. This algorithm uses sensitivity information to update both the Lagrange multipliers and design variables. Different from the conventional optimality criteria method, the proposed method does not satisfy constraints at every iteration. Rather, it improves the Lagrange multipliers and design variables such that the optimality criteria are satisfied upon convergence. The main advantages of the proposed method are its capability of handling multiple constraints and computational efficiency. In numerical examples, the proposed method was found to be more than 100 times faster than the optimality criteria method and more than 1000 times faster than the method of moving asymptotes.

A globally convergent modified multivariate version of the method of moving asymptotes

In this paper, we introduce an extension of our previous paper, A globally convergent version to the Method of Moving Asymptotes, in a multivariate setting. The proposed multivariate version is a globally convergent result for a new method, which consists iteratively of the solution of a modified version of the method of moving asymptotes. It is shown that the algorithm generated has some desirable properties. We state the conditions under which the present method is guaranteed to converge geometrically. The resulting algorithms are tested numerically and compared with several well-known methods.

Application of topological optimisation methodology to hydrodynamic thrust bearings

The bearing geometry has a big impact on the performance of a hydrodynamic thrust bearing. For this reason, shape optimisation of the bearing surface has been carried out for some time, with Lord Rayleigh’s early publication dated back to 1918. There are several recent results e.g. optimal bearing geometries that maximise the load carrying capacity for hydrodynamic thrust bearings. Currently, many engineers are making an effort to include sustainability in their work, which increases the need for bearings with lower friction and higher load carrying capacity. Improving these two qualities will result in lower energy consumption and increase the lifetime of applications, which are outcomes that will contribute to a sustainable future. For this reason, there is a need to find geometries that have performance characteristics of as low coefficient of friction torque as possible. In this work, the topological optimisation method of moving asymptotes is employed to optimise bearing geometries with the objective of minimising the coefficient of friction torque. The results are both optimised bearing geometries that minimise the coefficient of friction torque and bearing geometries that maximise the load carrying capacity. The bearing geometries are of comparable aspect ratios to the ones uses in recent publications. The present article also covers minimisation of friction torque on ring bearing geometries, also known as thrust washers. The results are thrust washers with periodical geometries, where the number of periodical segments has a high impact on the geometrical outcome.