• Steel and Composite Structures
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• v.51 no.4
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• pp.363-375
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• 2024

Within the optimization field, addressing the intricate posed by fluidic pressure loads on functionally graded structures with frequency-related designs is a kind of complex design challenges. This paper thus introduces an innovative density-based topology optimization strategy for frequency-constraint functionally graded structures incorporating Darcy's law and a drainage term. It ensures consistent treatment of design-dependent fluidic pressure loads to frequency-related structures that dynamically adjust their direction and location throughout the design evolution. The porosity of each finite element, coupled with its drainage term, is intricately linked to its density variable through a Heaviside function, ensuring a seamless transition between solid and void phases. A design-specific pressure field is established by employing Darcy's law, and the associated partial differential equation is solved using finite element analysis. Subsequently, this pressure field is utilized to ascertain consistent nodal loads, enabling an efficient evaluation of load sensitivities through the adjoint-variable method. Moreover, this novel approach incorporates load-dependent structures, frequency constraints, functionally graded material models, and polygonal meshes, expanding its applicability and flexibility to a broader range of engineering scenarios. The proposed methodology's effectiveness and robustness are demonstrated through numerical examples, including fluidic pressure-loaded frequency-constraint structures undergoing small deformations, where compliance is minimized for structures optimized within specified resource constraints.

• Steel and Composite Structures
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• v.51 no.3
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• pp.261-270
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• 2024

This paper proposes an effective method for optimizing the structure of functionally graded isotropic and incompressible linear elastic materials. The main emphasis is on utilizing a specialized polytopal composite finite element (PCE) technique capable of handling a broad range of materials, addressing common volumetric locking issues found in nearly incompressible substances. Additionally, it employs a continuum model for bi-directional functionally graded (BFG) material properties, amalgamating these aspects into a unified property function. This study thus provides an innovative approach that tackles diverse material challenges, accommodating various elemental shapes like triangles, quadrilaterals, and polygons across compressible and nearly incompressible material properties. The paper thoroughly details the mathematical formulations for optimizing the topology of BFG structures with various materials. Finally, it showcases the effectiveness and efficiency of the proposed method through numerous numerical examples.

• The Journal of Korea Robotics Society
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• v.8 no.3
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• pp.173-178
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• 2013

We present six-degree-of-freedom (6DoF) haptic rendering algorithms using translational ($PD_t$) and generalized penetration depth ($PD_g$). Our rendering algorithm can handle any type of object/object haptic interaction using penalty-based response and makes no assumption about the underlying geometry and topology. Moreover, our rendering algorithm can effectively deal with multiple contacts. Our penetration depth algorithms for $PD_t$ and $PD_g$ are based on a contact-space projection technique combined with iterative, local optimization on the contact-space. We circumvent the local minima problem, imposed by the local optimization, using motion coherence present in the haptic simulation. Our experimental results show that our methods can produce high-fidelity force feedback for general polygonal models consisting of tens of thousands of triangles at near-haptic rates, and are successfully integrated into an off-the-shelf 6DoF haptic device. We also discuss the benefits of using different formulations of penetration depth in the context of 6DoF haptics.