An approach for geometrically nonlinear topology optimization using moving wide-Bézier components with constrained ends

Standard moving morphable component (MMC)-based topology optimization methods use free components with explicitly geometrical parameters as design units to obtain the optimal structural topology by moving, deforming and covering such components. In this study, we intend to present a method for geometrically nonlinear explicit topology optimization using moving wide Bezier components with constrained ends. Not only can the method efficiently avoid the convergence issues associated with nonlinear structural response analysis, but it can also alleviate the component disconnection issues associated with the standard MMC-based topology optimization methods. The numerical investigations proposed in this work indicate that the proposed method allows us to obtain results in accordance with the current literature with a more stable optimization process. In addition, the proposed method can easily achieve minimum length scale control without adding constraints.

Optimizing Topology and Fiber Orientations With Minimum Length Scale Control in Laminated Composites

Discrete material optimization (DMO) has proven to be an effective framework for optimizing the orientation of orthotropic laminate composite panels across a structural design domain. The typical design problem is one of maximizing stiffness by assigning a fiber orientation to each subdomain, where the orientation must be selected from a set of discrete magnitudes (e.g., 0 deg, ±45 deg, 90 deg). The DMO approach converts this discrete problem into a continuous formulation where a design variable is introduced for each candidate orientation. Local constraints and penalization are then used to ensure that each subdomain is assigned a single orientation in the final solution. The subdomain over which orientation is constant is most simply defined as a finite element, ultimately leading to complex orientation layouts that may be difficult to manufacture. Recent literature has introduced threshold projections commonly used in density-based topology optimization into the DMO approach in order to influence the manufacturability of solutions. This work takes this idea one step further and utilizes the Heaviside projection method within DMO to provide formal control over the minimum length scale of structural features, holes, and patches of uniform orientation. The proposed approach is demonstrated on benchmark maximum stiffness design problems, and numerical results are near discrete with strict length scale control, providing a direct avenue to controlling the complexity of orientation layouts. This ultimately suggests that projection-based methods can play an important role in controlling the manufacturability of optimized material orientations.

Design Applicable 3D Microfluidic Functional Units Using 2D Topology Optimization with Length Scale Constraints

Due to the limits of computational time and computer memory, topology optimization problems involving fluidic flow frequently use simplified 2D models. Extruded versions of the 2D optimized results typically comprise the 3D designs to be fabricated. In practice, the depth of the fabricated flow channels is finite; the limited flow depth together with the no-slip condition potentially make the fluidic performance of the 3D model very different from that of the simplified 2D model. This discrepancy significantly limits the usefulness of performing topology optimization involving fluidic flow in 2D—at least if special care is not taken. Inspired by the electric circuit analogy method, we limit the widths of the microchannels in the 2D optimization process. To reduce the difference of fluidic performance between the 2D model and its 3D counterpart, we propose an applicable 2D optimization model, and ensure the manufacturability of the obtained layout, combinations of several morphology-mimicking filters impose maximum or minimum length scales on the solid phase or the fluidic phase. Two typical Lab-on-chip functional units, Tesla valve and fluidic channel splitter, are used to illustrate the validity of the proposed application of length scale control.

Optimizing Topology and Fiber Orientations With Minimum Length Scale Control in Laminated Composites

Discrete Material Optimization (DMO) has proven to be an effective framework for optimizing the orientation of orthotropic laminate composite panels across a structural design domain. The typical design problem is one of maximizing stiffness by assigning a fiber orientation to each subdomain, where the orientation must be selected from a set of discrete magnitudes (e.g., 0°, ±45°, 90°). The DMO approach converts this discrete problem into a continuous formulation where a design variable is introduced for each candidate orientation. Local constraints and SIMP style penalization are then used to ensure each subdomain is assigned a single orientation in the final solution. The subdomain over which orientation is constant is typically defined as a finite element, ultimately leading to complex orientation layouts that may be difficult to manufacture. Recent literature has introduced threshold projections, originally developed for density-based topology optimization, into the DMO approach in order to influence the manufacturability of solutions. This work takes this idea one step further and utilizes the Heaviside Projection Method within DMO to provide formal control over the minimum length scale of structural features, holes, and patches of uniform orientation. The proposed approach is demonstrated on benchmark maximum stiffness design problems in terms of objective function, solution discreteness, and manufacturability. Numerical results suggest that projection-based methods can play an important role in controlling the manufacturability of optimized material distributions in optimized design and that solutions are near-discrete with performance properties comparable to designs without manufacturing considerations.