Design-dependent Pressure Loads Research Articles

Frequency-constrained topology optimization in incompressible multi-material systems under design-dependent loads

In the realm of engineering design, structures grappling with fluidic pressure loads within precise frequency constraints necessitate innovative approaches. This study introduces a method to address the intricacies of design-dependent load-based structures, focusing on three key aspects: (i) managing structures constrained by frequency under fluidic pressure loads dependent on the design, (ii) integrating the use of multiple materials, and (iii) dealing with nearly incompressible materials. The proposed approach, detailed in this paper, employs polytopal composite finite elements (PCEs) to overcome the inherent volumetric locking phenomenon in incompressible materials. By incorporating Darcy’s law and a drainage term alongside the representative-solid phase, this approach ensures consistent treatment of fluidic pressure loads, dynamically adjusting their direction and location during the multi-material design process. The porosity of each element, intricately linked to its density variable through a Heaviside function, facilitates a smooth transition between solid and void phases. The application of Darcy’s law establishes a specific pressure field, solved using PCEs, enabling the computation of consistent nodal loads. This method simplifies the assessment of load sensitivities through the adjoint-variable technique. The method’s effectiveness and reliability are validated through numerical examples, demonstrating its capability to optimize compliance within specific volume constraints for frequency-limited structures subjected to design-dependent pressure loading and considering a diverse range of materials from compressible to nearly incompressible.

TOPress: a MATLAB implementation for topology optimization of structures subjected to design-dependent pressure loads

TOPress: a MATLAB implementation for topology optimization of structures subjected to design-dependent pressure loads

Bi-directional evolutionary topology optimization based on stress minimization under design-dependent surface loads

This article proposes an approach for structural topology optimization based on stress, under design-dependent surface loads. The algorithm has been developed by adapting the stress minimization version of the bi-directional evolutionary structural optimization method, with the inclusion of surface loads. The P-norm of von Mises stress is used as an aggregate function and volume constraints are employed. The stresses have been obtained using the finite element method applied to the continuum bi-dimensional elastic structures. The sensitivity analysis has been carried out by the adjoint method, including design-dependent surface loads. Three examples have been investigated. The first is the piston head problem, a benchmark for design-dependent pressure loads. In this example, the algorithm convergence is demonstrated. The other two are benchmarks for stress-based problems: the simply supported beam and the L-bracket. The proposed method is shown to be effective in reducing the maximum stress, generating easily manufacturable topologies.

Topology optimization of compliant mechanisms and structures subjected to design-dependent pressure loadings

This article presents an extended algorithm for topology optimization of compliant mechanisms and structures with design-dependent pressure loadings using the moving iso-surface threshold (MIST) method. In this algorithm, the fluid-structure interface is modeled using the finite element method via considering equivalent virtual strain energy and work and is tracked by an element-based searching scheme. Design-dependent pressure loads are directly applied on interface boundary and are calculated as virtual work equivalent nodal forces in the interface elements based on the finite element formulation. Several numerical examples are presented for topology optimization of mean compliance and compliant mechanisms. The present algorithm is validated through benchmarking with the results in literature and/or full finite element analysis (FEA) results of the optimum compliant mechanism and structure designs.

Topology optimization of structures under design-dependent pressure loads by a boundary identification-load evolution (BILE) model

When a structure under design-dependent pressure loads is being topologically optimized, the magnitude and/or direction of these loads may change as the structure’s topology is being updated simultaneously. Therefore, two critical aspects in the optimization to be addressed are the identification of changing topological boundaries and the correct application of pressure loads to newly formed pressure surfaces. In this study, we present a simple boundary identification and load evolution (BILE) model to resolve these aspects. As the name suggests, a boundary identification step utilizes a threshold volume fraction to define topological boundaries and a load evolution step that occurs for a number of iterations between two successive boundary identification iterations. This model is particularly attractive because of its ease of application and computational cost-effectiveness as most numerical results for 2D problems using 5000 to 13,000 isoparametric quad elements were obtained under 90 s and 100 iterations using the optimality criteria method (OCM). Based on the modified SIMP method, this model is compared with existing methodologies by presenting several numerical examples for validation.

Level set topology optimization for design-dependent pressure loads using the reproducing kernel particle method

This paper presents a level set topology optimization method in combination with the reproducing kernel particle method (RKPM) for the design of structures subjected to design-dependent pressure loads. RKPM allows for arbitrary particle placement in discretization and approximation of unknowns. This attractive property in combination with the implicit boundary representation given by the level set method provides an effective framework to handle the design-dependent loads by moving the particles on the pressure boundary without the need of remeshing or special numerical treatments. Moreover, the reproducing kernel (RK) smooth approximation allows for the Young’s modulus to be interpolated using the RK shape functions. This is another advantage of the proposed method as it leads to a smooth Young’s modulus distribution for smooth boundary sensitivity calculation which yields a better convergence. Numerical results show good agreement with those in the literature.

Optimal Design of Soft Pneumatic Bending Actuators Subjected to Design-Dependent Pressure Loads

Soft actuators, mainly composed of soft materials, have made a great impact on applications in unstructured or unknown environments due to their high flexibility and customizability. The design methods of soft actuators can be divided into two groups: the bionic design method and the topology optimization method. Compared to the bionic design method that requires numerous experiments, the topology optimization method can generate innovative structures according to the design requirements. However, the existing topology optimization method cannot be applied to soft pneumatic bending actuator (SPBA) designs because SPBAs are usually subjected to design-dependent pressure loads of which the position depends on the structure. In this paper, we propose an optimal design framework of SPBAs to resolve the design-dependent load problem using an adaptive bi-directional evolutionary structural optimization method. Herein, SPBAs are considered as compliant mechanisms and our goal is to achieve maximum bending deformation as well as structural stiffness. In finite element analysis, each element in the design domain is set to solid or void according to sensitivity number, which is approximated by the objective function derivative with respect to the design variables. During the iterative optimization procedure, we explicitly define the movable solid-void boundary surfaces on which the pressure will act. A precision prototype actuator is fabricated, and its performance is evaluated in terms of free travel experiment. Some extensions are supplied to validate the optimality and reliability of the proposed method. This framework paves a way for the diversity of soft actuators.

Stress-constrained level set topology optimization for design-dependent pressure load problems

This work presents a level set framework to solve topology optimization problems subject to local stress constraints considering design-dependent pressure loads. Two technical difficulties are related to this problem. The first one is the local nature of stresses. To deal with this issue, stress constraints are included to the problem by means of an Augmented Lagrangian scheme. The second is the adequate association between the moving boundary and the pressure acting on it. This difficulty is easily overcome by the level set method that allows for a clear tracking of the boundary along the optimization process. In the present approach, a reaction–diffusion equation substitutes the classical Hamilton–Jacobi equation to control the level set evolution. This choice has the advantage of allowing the nucleation of holes inside the domain and the elimination of the undesirable level set reinitializations. In addition, the optimization algorithm allows the rupture of loading boundaries, that is, the crossing of the pressured (wet) boundary with the traction free boundary is not avoided. This gives more freedom to the algorithm for topological changes. In order to validate the proposed scheme against stress concentrations, all numerical examples are performed on constrained domains containing singularities. Moreover, optimized designs obtained from stress-constrained and compliance problems are compared.

On the effect of fluid-structure interactions and choice of algorithm in multi-physics topology optimisation

This article presents an optimisation framework for the compliance minimisation of structures subjected to design-dependent pressure loads. A finite element solver coupled to a Lattice Boltzmann method is employed, such that the effect of the fluid-structure interactions on the optimised design can be considered. It is noted that the main computational expense of the algorithm is the Lattice Boltzmann method. Therefore, to improve the computational efficiency and to assess the effect of the fluid-structure interactions on the final optimised design, the degree of coupling is changed.Several successful topology optimisation algorithms exist with thousands of associated publications in the literature. However, only a small portion of these are applied to real-world problems, with even fewer offering a comparison of methodologies. This is especially important for problems involving fluid-structure interactions, where discrete and continuous methods can provide different advantages.The goal of this research is to couple two key disciplines, fluids and structures, into a topology optimisation framework, which shows fast convergence for multi-physics optimisation problems. This is achieved by offering a comparison of three popular, but competing, optimisation methodologies. The needs for the exploration of larger design spaces and to produce innovative designs make meta-heuristic algorithms less efficient for this task. A coupled analysis, where the fluid and structural mechanics are updated, provides superior results compared with an uncoupled analysis approach, however at some computational expense. The results in this article show that the method is sensitive to whether fluid-structure coupling is included, i.e. if the fluid mechanics are updated with design changes, but not to the degree of the coupling, i.e. how regularly the fluid mechanics are updated, up to a certain limit. Therefore, the computational efficiency of the algorithm can be considerably increased with small penalties in the quality of the objective by relaxing the coupling.

Topology optimization for submerged buoyant structures

ABSTRACTThis paper presents an evolutionary structural topology optimization method for the design of completely submerged buoyant modules with design-dependent fluid pressure loading. This type of structure is used to support offshore rig installation and pipeline transportation at all water depths. The proposed optimization method seeks to identify the buoy design that has the highest stiffness, allowing it to withstand deepwater pressure, uses the least material and has a minimum prescribed buoyancy. Laplace's equation is used to simulate underwater fluid pressure, and a polymer buoyancy module is considered to be linearly elastic. Both domains are solved with the finite element method. Using an extended bi-directional evolutionary structural optimization (BESO) method, the design-dependent pressure loads are modelled in a straightforward manner without any need for pressure surface parametrization. A new buoyancy inequality constraint sets a minimum required buoyancy effect, measured by the joint volume of the structure and its interior voids. Solid elements with low strain energy are iteratively removed from the initial design domain until a certain prescribed volume fraction. A test case is described to validate the optimization problem, and a buoy design problem is used to explore the features of the proposed method.

Structural topology optimization with design-dependent pressure loads

One way to solve topology optimization of continuum structures under design-dependent pressure loads is to recover the loading surface at each step of the minimization process. During the topology evolution, the intermediate topologies obtained by using the SIMP (Solid Isotropic Material with Penalization) method actually can be regarded as gray scale images, for which the paper proposes a new material boundary identification scheme based on image segmentation technique. The Distance Regularized Level Set Evolution (DRLSE) method proposed by Li et al., IEEE Trans Image Process 19(12):3243---3254 (2010) is utilized to detect the image edge. Then the pressure boundary is represented as the zero level contour of a level set function (LSF). Inheriting the merits of the level set method, the current scheme can handle the topological change of the pressure boundary efficiently and be easily extended to the three-dimensional problems. In addition, the scheme is more stable compared with the conventional loading surface searching methods since it works well for the intermediate topologies with local scattered densities. A new optimization framework is also proposed to avoid the load sensitivity analysis. Four numerical examples are presented to show the validity and advantages of the proposed scheme.

Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems

This article presents an evolutionary topology optimization method for compliance minimization of structures under design-dependent pressure loads. In traditional density based topology optimization methods, intermediate values of densities for the solid elements arise along the iterations. Extra boundary parametrization schemes are demanded when these methods are applied to pressure loading problems. An alternative methodology is suggested in this article for handling this type of load. With an extended bi-directional evolutionary structural optimization method associated with a partially coupled fluid–structure formulation, pressure loads are modelled with hydrostatic fluid finite elements. Due to the discrete nature of the method, the problem is solved without any need of pressure load surfaces parametrization. Furthermore, the introduction of a separate fluid domain allows the algorithm to model non-constant pressure fields with Laplace's equation. Three benchmark examples are explored in order to show the achievements of the proposed method.

Structural topology optimization with design-dependent pressure loads

This paper presents an approach for the topology optimization of structures under design-dependent pressure loading. Compared with traditional optimization problems with a fixed load, in a design-dependent load problem, the location, direction, and magnitude of the load change with respect to the design at every iteration. Using the SIMP model, the current method proposes a material boundary identification scheme by iteratively connecting points of equal density, with the use of a predefined void region. This predefined void region allows the structure to be loaded by pressure from outside the domain, as well as by pressure that is completely enclosed within the domain. This is particularly useful when there are multiple pressure vessels that can be interacting, or when symmetry cannot be used to bisect the pressure vessel. Also, by using an iso-density line to define the boundary, no additional artificial parameters that might affect the final solution are needed. An analytical method for deriving the sensitivity of the loads is also presented; this is an alternative to the finite-difference method and it could reduce the number of function calls. Numerical examples are presented to show the advantages and robustness of the proposed method.

Reply to the discussion on “Topology optimization with design-dependent pressure loading”

This article is a reply to the discussion on our paper “Topology Optimization of Energy Harvesting Devices Using Piezoelectric Material” by Prof. Silva. There are several comments raised in the discussion and they have all been addressed in this article. The authors believe this response clarify all unclear points in our paper and is useful to the technical community.

Topology optimization of multiphase material structures under design dependent pressure loads

In this paper, design-dependent pressure loads are addressed for topology optimization problems of multiphase material structures. The modeling of unidirectional load distribution with respect to the material density is studied and mathematical formulations of exponential form are established for the first time to model unidirectional pressure loads on the moving surface and contact surface of fixed shape, respectively. In both load cases, sensitivity analysis scheme of the structural compliance is developed to show the effects of the design-dependent loads. By means of 2D and 3D numerical examples, comparative studies are performed in detail to show the effects of different load cases upon the optimal configurations. It is seen that the proposed design procedure is reliable to deal with the design-dependent load cases.

Topology optimization of multiphase material structures under design dependent pressure loads

Topology optimization of multiphase material structures under design dependent pressure loads

Topology optimization with design-dependent pressure loading

In this paper, the layout of structures under design-dependent pressure loading is optimized using a topology optimization approach. In contrast to topology optimization problems with conventional static external loading, the position and direction of pressure loading are changing with topology of structure during optimization iterations. In order to model the changing structural surface boundaries under design-dependent pressure loading, a pseudo equal-potential function is introduced. Design sensitivity analysis is derived from the adjoint method. Three examples solved by the proposed method are presented.