The Boundary Smoothing in Discrete Topology Optimization of Structures

2013 ◽  
Author(s):  
Hong Zhou ◽  
Shabaz Ahmed Mohammed
Keyword(s):  
Topology Optimization ◽  
Design Domain ◽  
Discrete Topology ◽  
Corner Cutting ◽  
Outer Corner ◽  
Material State ◽  
Corner Filling ◽  
Boundary Smoothing ◽  
Design Cell

In discrete topology optimization, material state is either solid or void and there is no topology uncertainty caused by intermediate material state. A common problem of the current discrete topology optimization is that boundaries are unsmooth. Unsmooth boundaries are caused by corners in topology solutions. Although the outer corner cutting and inner corner filling strategy can mitigate corners, it cannot eliminate them. 90-degree corners are usually mitigated to 135-degree corners under the corner handling strategy. The existence of corners in topology solutions is because of the subdivision model. If regular triangles are used to subdivide design domains, corners are inevitable in topology solutions. To eradicate corner from any topology solution, a subdivision model is introduced in this paper for the discrete topology optimization of structures. The design domain is discretized into quadrilateral design cells and every quadrilateral design cell is further subdivided into triangular analysis cells that have a curved hypotenuse. With the presented subdivision model, all boundaries and connections are smooth in any topology solution. The proposed subdivision approach is demonstrated by two discrete topology optimization examples of structures.

Corner Elimination in Discrete Topology Optimization of Compliant Mechanisms

2013 ◽  
Author(s):  
Hong Zhou ◽  
Venkat S. Jangam
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Design Domain ◽  
Discrete Topology ◽  
Corner Cutting ◽  
Outer Corner ◽  
Material State ◽  
Corner Filling ◽  
Design Cell

In discrete topology optimization, material state is either solid or void and there is no topology uncertainty caused by intermediate material state. A common problem of the current discrete topology optimization is that boundaries are unsmooth. Unsmooth boundaries are caused by the corners in topology solutions. Although outer corner cutting and inner corner filling strategy can mitigate corners, it cannot eliminate them. 90-degree corners are usually mitigated to 135-degree corners under the corner handling strategy. The existence of corners in topology solutions is because of the subdivision model. If regular triangles are used to subdivide a design domain, corners are inevitable in topology solutions. To eradicate corner from any topology solution, an innovative subdivision model is introduced in this paper for discrete topology optimization of compliant mechanisms. A design domain is discretized into quadrilateral design cells and every quadrilateral design cell is further subdivided into special triangular analysis cells that have a curved hypotenuse. With the presented subdivision model, all boundaries are smooth in any topology solution. Two discrete topology optimization examples of compliant mechanisms are solved based on the proposed subdivision approach.

The Discrete Topology Optimization of Compliant Mechanisms

2012 ◽  
Author(s):  
Hong Zhou ◽  
Chandrasekhar M. Ayyalasomayajula
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Local Stress ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Outer Corner ◽  
Material State ◽  
Corner Filling ◽  
Design Cell

In the discrete topology optimization, material state is either solid or void and there is no topology uncertainty problem caused by intermediate material state. The outer corner cutting and inner corner filling strategy is introduced in this paper for the discrete topology optimization of compliant mechanisms. The design domain is discretized into quadrilateral design cells and every quadrilateral design cell is further subdivided into triangular analysis cells. All outer and inner corners are eliminated with the corner handling strategy. To make the designed compliant mechanisms safe, the local stress constraint is directly imposed on each triangular analysis cell. To circumvent the geometrical bias against the vertical design cells, the binary bit-array genetic algorithm is used to search for the optimal topology. Two topology optimization examples of compliant mechanisms are solved based on the proposed corner handling strategy and subdivision approach.

Discrete Topology Optimization of Structures Without Uncertainty

2013 ◽  
Author(s):  
Hong Zhou ◽  
Surya Tej Kolavennu
Keyword(s):  
Topology Optimization ◽  
Optimization Procedure ◽  
Design Domain ◽  
Discrete Topology ◽  
Optimization Strategy ◽  
Dependence Problem ◽  
Material State ◽  
Multiple Loading ◽  
Hybrid Discretization ◽  
Design Cell

The topology of a structure is defined by its genus or number of handles. When the topology of a structure is optimized, its topology might be changed if the material state of a design cell is switched from solid to void or vice versa. In discrete topology optimization, each design cell is either solid or void and there is no topology uncertainty from any grey design cell. Point connection might cause topology uncertainty and is eradicated when hybrid discretization model is used for discrete topology optimization. However, the topology solution of an optimized structure might be uncertain when its design domain is discretized differently, which is commonly called mesh dependence problem. In this paper, the degree of genus based topology optimization strategy is introduced to circumvent this topology uncertainty. With this strategy, the genus of an optimized structure is constrained during its topology optimization process. There is no topology uncertainty even if different design domain discretizations are used. The introduced strategy is used for discrete topology optimization of structures that have multiple loading points in this paper. The presented discrete topology optimization procedure is demonstrated by examples with different degrees of genus and loading conditions.

The Discrete Topology Optimization of Structures Using the Improved Hybrid Discretization Model

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Hong Zhou ◽  
Rutesh B. Patil
Keyword(s):  
Topology Optimization ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Design Domain ◽  
Discrete Topology ◽  
Material State ◽  
Hybrid Discretization ◽  
Design Cell

In the discrete topology optimization, material state is either solid or void and there is no topology uncertainty caused by any intermediate material state. In this paper, the improved hybrid discretization model is introduced for the discrete topology optimization of structures. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into triangular analysis cells. The dangling and redundant solid design cells are completely eliminated from topology solutions in the improved hybrid discretization model to avoid sharp protrusions. The local stress constraint is directly imposed on each triangular analysis cell to make the designed structure safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. The presented discrete topology optimization procedure is illustrated by two topology optimization examples of structures.

The Improved Hybrid Discretization Model for the Discrete Topology Optimization of Compliant Mechanisms

2012 ◽  
Author(s):  
Hong Zhou ◽  
Nisar Ahmed ◽  
Avinash Uttha
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Local Stress ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Material State ◽  
Material Utilization ◽  
Hybrid Discretization ◽  
Design Cell

In the discrete topology optimization, material state is either solid or void and there is no topology uncertainty problem caused by any intermediate material state. In this paper, the improved hybrid discretization model is introduced for the discrete topology optimization of compliant mechanisms. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into triangular analysis cells. The dangling and redundant solid design cells are removed from topology solutions in the improved hybrid discretization model to promote the material utilization. To make the designed compliant mechanisms safe, the local stress constraint is directly imposed on each triangular analysis cell. To circumvent the geometrical bias against the vertical design cells, the binary bit-array genetic algorithm is used to search for the optimal topology. Two topology optimization examples of compliant mechanisms are solved based on the proposed improved hybrid discretization model to verify its effectiveness.

The Improved Quadrilateral Discretization Model for the Discrete Topology Optimization of Structures

2012 ◽  
Author(s):  
Hong Zhou ◽  
Anil K. Annepu
Keyword(s):  
Topology Optimization ◽  
Local Stress ◽  
Optimization Method ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Sharp Corner ◽  
Material State ◽  
Material Utilization ◽  
Design Cell

In the discrete topology optimization, material state is either solid or void and there is no topology uncertainty problem caused by intermediate material state. In this paper, the improved quadrilateral discretization model is introduced for the discrete topology optimization of structures. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into 16 triangular analysis cells. All kinds of dangling quadrilateral design cells and sharp-corner triangular analysis cells are removed in the improved quadrilateral discretization model to promote the material utilization. To make the designed structures safe, the local stress constraint is directly imposed on each triangular analysis cell. To circumvent the geometrical bias against the vertical design cells, the binary bit-array genetic algorithm is used to search for the optimal topology. The effectiveness of the proposed improved quadrilateral discretization model and its related discrete topology optimization method is verified by two topology optimization examples of structures.

The Uncertainty Elimination in Discrete Topology Optimization of Compliant Mechanisms

2013 ◽  
Author(s):  
Hong Zhou ◽  
Satya Raviteja Kandala
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Process ◽  
Design Domain ◽  
Discrete Topology ◽  
Optimization Strategy ◽  
Hybrid Discretization ◽  
Ambiguous Point

Topology uncertainty leads to different topology solutions and makes topology optimization ambiguous. Point connection and grey cell might cause topology uncertainty. They are both eradicated when hybrid discretization model is used for discrete topology optimization. A common topology uncertainty in the current discrete topology optimization stems from mesh dependence. The topology solution of an optimized compliant mechanism might be uncertain when its design domain is discretized differently. To eliminate topology uncertainty from mesh dependence, the genus based topology optimization strategy is introduced in this paper. The topology of a compliant mechanism is defined by its genus which is the number of holes in the compliant mechanism. With this strategy, the genus of an optimized compliant mechanism is actively controlled during its topology optimization process. There is no topology uncertainty when this strategy is incorporated into discrete topology optimization. The introduced topology optimization strategy is demonstrated by examples with different degrees of genus.

Optimizing the Topologies of Compliant Mechanisms Using the Improved Modified Quadrilateral Discretization Model

2012 ◽  
Author(s):  
Hong Zhou ◽  
Venkata Krishna Perivilli ◽  
Praveen Chilukuri
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Local Stress ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Sharp Corner ◽  
Material Utilization ◽  
Design Cell

The improved modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into 16 triangular analysis cells. All kinds of dangling full and half quadrilateral design cells and sharp-corner triangular analysis cells are removed in the improved modified quadrilateral discretization model to enhance the material utilization. Every quadrilateral design cell or triangular analysis cell is either solid or void to implement the discrete topology optimization and eradicate topology uncertainty caused by intermediate material states. The local stress constraint is directly imposed on each triangular analysis cell to make the synthesized compliant mechanism safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. Two topology optimization examples of compliant mechanisms are solved based on the proposed improved modified quadrilateral discretization model to verify its effectiveness.

Topology Optimization of Compliant Mechanisms Using the Improved Quadrilateral Discretization Model

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Hong Zhou ◽  
Avinash R. Mandala
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Local Stress ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Sharp Corner ◽  
Material Utilization ◽  
Design Cell

The improved quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into triangular analysis cells. All kinds of dangling quadrilateral design cells and sharp-corner triangular analysis cells are removed in the improved quadrilateral discretization model to promote the material utilization. Every quadrilateral design cell or triangular analysis cell is either solid or void to implement the discrete topology optimization and eradicate the topology uncertainty caused by intermediate material states. The local stress constraint is directly imposed on each triangular analysis cell to make the synthesized compliant mechanism safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. Two topology optimization examples of compliant mechanisms are solved based on the proposed improved quadrilateral discretization model to verify its effectiveness.

The Discrete Topology Optimization of Structures Using the Modified Quadrilateral Discretization Model

2012 ◽  
Author(s):  
Hong Zhou ◽  
Ravinder G. Malela
Keyword(s):  
Topology Optimization ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Optimal Topology ◽  
Stress Constraint ◽  
Discrete Topology ◽  
Cell Problem ◽  
Design Variables ◽  
Design Cell

The modified quadrilateral discretization model is introduced for the discrete topology optimization of structures in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical or diagonal direction. Point connection is eradicated. In the proposed discrete topology optimization method of structures, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the optimized structure safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented discrete topology optimization procedure is illustrated by two topology optimization examples of structures.

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