Shape optimization of the cavitator for a supercavitating torpedo

The study of reactive silencers by shape and parametric optimization techniques

This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending.

8 - Shape optimization of dental restorations

ABSTRACTIn injection molding processes, shrinkage and warpage cause deviations in the size and shape of produced parts compared to the cavity shape. While shrinkage is due to the change of material density during solidification, warpage is caused by uneven cooling and internal stresses within the part. One approach to mitigate these effects is by adjusting the cavity shape to anticipate the deformation. While finding the optimal cavity shape is often experience‐based in practice, numerical design optimization can greatly assist in this process. In this study, we evaluate various numerical algorithms from existing literature to identify the optimal cavity shape. Each method is briefly outlined regarding how it adapts the geometry, and we discuss their respective strengths and weaknesses for different scenarios. We conduct comparisons using 3D geometries of varying complexity. Our findings demonstrate that, for geometric warpage compensation, the node‐based reverse geometry method yields the least warpage and is computationally cost‐effective. Furthermore, it is straightforward to implement and consistently performs well across different geometries.

Horizontal penetration in granular media is ubiquitous, from tunneling and geotechnical site investigation, to root growth and the locomotion of burrowing animals in nature. This contribution couples the discrete element method (DEM) with ant colony optimisation, a heuristic optimisation algorithm, to find the optimal tip shapes to minimise drag and lift forces during horizontal penetration. The tip which minimizes drag has a slender profile with a low tip curvature, to give a drag force that is $$15.6\%$$ 15.6 % lower compared to a conventional CPT intruder, however this shape induces a downwards force that increases with intruder depth. Conversely, the tip that minimizes lift is blunt, with a high tip curvature and short width, and reduces the drag and lift forces by $$4.5\%$$ 4.5 % and $$30.8\%$$ 30.8 % (respectively) compared to the CPT. The lift and drag forces are competing optimisation objectives, thus the tip shape with the optimal trade-off between drag and lift forces can be established using Pareto optimality. The Pareto optimal tip shape reduces the drag and lift forces by $$10.7\%$$ 10.7 % and $$19.4\%$$ 19.4 % respectively, and is strikingly similar to the profile of a sandfish. This contribution shows that when a common goal exists, bio-inspired solutions can offer an optimal solution to engineering applications. We also show the potential to integrate DEM simulations within an optimization framework to develop innovative design solutions.

The population of the world is increasing day by day. Accordingly, the amount of production and consumption are increasing. Due to the continuous and rapid development of technology, the duration of the use of some products becomes shorter. That is why the more efficient use of limited resources is even more important. In the developing and growing automotive industry, companies are currently focusing on weight and cost reduction methods to compete. In this study, the optimum design has been achieved by using topology and shape optimization in the suspension cover used in suspension systems. As a result of the topology and shape optimization efforts, The mass of the optimum design achieved was reduced by 35.203 % according to the first design.

The design of a compact superconducting crab-cavity for LHC using Nb-on-Cu-coating technique is presented. The cavity shape is based on the ridged waveguide resonator with wide open apertures to provide access to the inner surface of the cavity for coating. It also provides natural damping for HOMs and rather low longitudinal and transverse impedances. The results of the cavity shape optimization taking into account RF performance, coating, and thermo-mechanical considerations as well as the design and fabrication plans of the first prototype for coating and cold tests are presented.

The design of a centrifugal compressor for supercritical carbon dioxide power cycle must consider non-ideal gas effects and the possible occurrence of two-phase flows. Shape optimization techniques, combined with computational fluid-dynamic (CFD) simulations, can produce optimized designs while inherently coping with such peculiar flow characteristics. This study presents a three-dimensional shape optimization of a compressor stage composed of the impeller and the vaneless diffuser, whose compression starts close to the critical point. Impeller blade angle distributions and meridional channel are parameterized with Bezier control points, enabling local shape control within the optimization routine. The pinch of the vaneless diffuser is also optimized. The experimentally validated CFD solver considers both non-ideal effects and two-phase homogeneous flows, assuming thermodynamic equilibrium and a barotropic fluid. The constrained optimization problem is addressed using genetic algorithms. To mitigate computational costs, Kriging surrogates for the objective function and constraints are trained using a limited number of CFD results. The optimized geometry shows an appreciable efficiency increase (1.1 percentage points) while delivering the design pressure ratio. Although performing better at the design condition, the operating range of the compressor is altered by the optimization. Future optimizations that include both design and off-design operating points in the definition of the objective function and constraints may mitigate this problem.

In this paper, the moving element method (MEM) is extended to cooperate with the boundary element method (BEM), namely, the BEM-MEM. This method is applied to compute hydroelastic responses of a pontoon type very large floating structure (VLFS) under wave action and also subjected to a moving load. By using this method, the structure is discretized into “moving elements” which are conceptual elements and “flow” with the moving load. Thus, the proposed method eliminates the need for keeping track of the location of the moving load with respect to the floating structure. The surrounding fluid is defined based on the potential flow theory and the motion of the floating plate is governed by the vibration equation of a thin plate. The governing equations of motion, as well as structural matrices of moving element and fluid matrices of boundary element are formulated in a relative coordinate system traveling at a constant speed. The numerical results conducted by using the BEM-MEM are compared with the results obtained by alternative approaches. The paper also discusses the effect of water depth on responses of the floating structure including displacements and drag force.

The angular momentum balance is solved numerically for a size 29 mm CarboMedics prosthetic heart valve. The lift force is estimated from potential flow theory, while the drag force is estimated from the lift force and a blunt body empiricism. Buoyancy and gravitational effects are calculated based on the assumption of homogeneous leaflets. Other assumptions include uniform flow, negligible friction at the pivot axis, negligible viscous damping and fluid inertance, and a symmetry flow condition. Oscillations are predicted in the opening dynamics in the range of 2-25 Hz, for flow rates through one-half of the orifice in the range of 0.1-10.0 l/min. The frequency of these oscillations is dependent upon the orientation of the leaflet in relation to the gravitational field and the magnitude of the flow rate. In vivo and in vitro measurements by other investigators demonstrate similar effects of gravity and flow rate, with flutter frequencies of the order of 10-100 Hz. Excitation frequencies, based on vortex shedding, are estimated to be of the order 2-200 Hz, for the range of flow rates of the theoretical model. These results suggest that the natural frequency of this rotational second order system may, in theory, be a contributing factor to the flutter observed in bileaflet cardiac valve prostheses. The clinical significance of this finding is yet to be established.

In this paper, the blockage effects on a rectangular antenna are investigated through numerical simulation, and a correction method for the wind load coefficients is presented. In terms of the separation pressure measured by the wind tunnel test and the law of separation pressure with blockages achieved from the numerical simulation, we derive a relationship for base pressure coefficient of the rectangular antenna with various blockages. Adopting the formula based on the potential flow theory, the drag coefficient without blockage can be obtained. Using the base pressure coefficient to re-normalise the pressure coefficient, the characteristic that the re-normalised pressure coefficient the antenna is independent of the blockage ratio is verified. Furthermore, the pressure distributions on the rectangular antenna without blockage are obtained by the re-normalised pressure coefficient. The corrected results show that the blockage effect on pressure and drag force on the rectangular antenna both are removed effectively.

To establish an alternative analytical framework for the elastic-wave imaging of underground cavities, the focus of this study is an extension of the concept of topological derivative, rooted in elastostatics and shape optimization, to three-dimensional elastodynamics involving semi-infinite and infinite solids. The main result of the proposed boundary integral approach is a formula for topological derivative, explicit in terms of the elastodynamic fundamental solution, obtained by an asymptotic expansion of the misfit-type cost functional with respect to the creation of an infinitesimal hole in an otherwise intact (semi-infinite or infinite) elastic medium. Valid for an arbitrary shape of the infinitesimal cavity, the formula involves the solution of six canonical exterior elastostatic problems, and becomes fully explicit when the vanishing cavity is spherical. A set of numerical results is included to illustrate the potential of topological derivative as a computationally efficient tool for exposing an approximate cavity topology, location, and shape via a grid-type exploration of the host solid. For a comprehensive solution to three-dimensional inverse scattering problems involving elastic waves, the proposed approach can be used most effectively as a pre-conditioning tool for more refined, albeit computationally intensive minimization-based imaging algorithms. To the authors' knowledge, an application of topological derivative to inverse scattering problems has not been attempted before; the methodology proposed in this paper could also be extended to acoustic problems.

PurposeState-of-the-art medical examination techniques (e.g., rhinomanometry and endoscopy) do not always lead to satisfactory postoperative outcome. A fully automatized optimization tool based on patient computer tomography (CT) data to calculate local pressure gradient regions to reshape pathological nasal cavity geometry is proposed.MethodsFive anonymous pre- and postoperative CT datasets with nasal septum deviations were used to simulate the airflow through the nasal cavity with lattice Boltzmann (LB) simulations. Pressure gradient regions were detected by a streamline analysis. After shape optimization, the volumetric difference between the two shapes of the nasal cavity yields the estimated resection volume.ResultsAt LB rhinomanometry boundary conditions (bilateral flow rate of 600 ml/s), the preliminary study shows a critical pressure gradient of −1.1 Pa/mm as optimization criterion. The maximum coronal airflow ΔA := cross-section ratio frac{mathrm{virtual surgery }}{mathrm{post}-mathrm{surgery}} found close to the nostrils is 1.15. For the patients a pressure drop ratio ΔΠ := (pre-surgery − virtual surgery)/(pre-surgery − post-surgery) between nostril and nasopharynx of 1.25, 1.72, −1.85, 0.79 and 1.02 is calculated.ConclusionsLB fluid mechanics optimization of the nasal cavity can yield results similar to surgery for air-flow cross section and pressure drop between nostril and nasopharynx. The optimization is numerically stable in all five cases of the presented study. A limitation of this study is that anatomical constraints (e.g. mucosa) have not been considered.

Optimal rigid and porous material distributions for noise barrier by acoustic topology optimization

In this paper, shape optimization is employed to improve the stability of the flow past an elastically mounted circular cylinder at subcritical Reynolds numbers (Re < 47). As a key criterion for the stability of fluid-structure interaction system, dynamic derivative is adopted as the object of the optimization. The parametrization of the cross section is based on the class-shape function transformation technique. Then, shape optimization is conducted using the differential evolution algorithm. To improve the optimization efficiency, a surrogate model is constructed to replace the direct numerical simulation in the optimization process. Research shows that through the shape optimization, vortex-induced vibration is significantly suppressed and the stability of the fluid-structure interaction system is remarkably improved. In addition, the critical Reynolds number of the optimized cross section is also improved compared with that of the circular cylinder.