scholarly journals On transmissible load formulations in topology optimization

2021 ◽  
Author(s):  
Hongjia Lu ◽  
Andrew Tyas ◽  
Matthew Gilbert ◽  
Aleksey V. Pichugin
Keyword(s):  
Topology Optimization ◽  
Analytical Solution ◽  
Load Application ◽  
Optimal Structure ◽  
Optimization Process ◽  
Numerical Examples ◽  
Cantilever Structure ◽  
External Loads ◽  
Surface Loads ◽  
Mohr’S Circle

AbstractTransmissible loads are external loads defined by their line of action, with actual points of load application chosen as part of the topology optimization process. Although for problems where the optimal structure is a funicular, transmissible loads can be viewed as surface loads, in other cases such loads are free to be applied to internal parts of the structure. There are two main transmissible load formulations described in the literature: a rigid bar (constrained displacement) formulation or, less commonly, a migrating load (equilibrium) formulation. Here, we employ a simple Mohr’s circle analysis to show that the rigid bar formulation will only produce correct structural forms in certain specific circumstances. Numerical examples are used to demonstrate (and explain) the incorrect topologies produced when the rigid bar formulation is applied in other situations. A new analytical solution is also presented for a uniformly loaded cantilever structure. Finally, we invoke duality principles to elucidate the source of the discrepancy between the two formulations, considering both discrete truss and continuum topology optimization formulations.

Structural Topology Optimization Using a Moving Morphable Component-Based Method Considering Geometrical Nonlinearity

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Benliang Zhu ◽  
Qi Chen ◽  
Rixin Wang ◽  
Xianmin Zhang
Keyword(s):  
Topology Optimization ◽  
Design Problem ◽  
Strong Influence ◽  
Geometrical Nonlinearity ◽  
Optimization Process ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Numerical Examples

The moving morphable component (MMC)-based method is a newly developed approach for topology optimization. In the MMC-based method, the design problem is formulated using a set of morphable components, and the optimized structural topologies are obtained by optimizing shapes, sizes, and locations of these components. However, the optimization process often tends to break the connection between the load area and the supported boundary. This disconnection has a strong influence on the convergence, especially when the large deformation effects are considered. In this paper, a method is developed for topology optimization of geometrically nonlinear structures by using the MMC-based method. A scheme is developed to address the disconnection issue in the optimization process. Several numerical examples are used to demonstrate the validity of the proposed method.

Inclined Loading Capacity of Embedded Suction Anchors in Clay

2009 ◽  
Author(s):  
Y. S. Kim ◽  
K. O. Kim ◽  
Y. Cho ◽  
S. Bang ◽  
K. D. Jones
Keyword(s):  
Analytical Solution ◽  
Model Test ◽  
Inclination Angle ◽  
Load Application ◽  
Centrifuge Model Test ◽  
Loading Capacity ◽  
Test Results ◽  
Pullout Capacity ◽  
Centrifuge Model ◽  
Inclined Loading

An analytical solution has been developed to estimate the inclined pullout capacity of an embedded suction anchor in clay seafloor. Validation has been made through comparisons with a limited number of centrifuge model test results. Results indicate that the inclined pullout capacity of an embedded suction anchor in clay decreases as the load inclination angle to the horizontal increases. As the point of the load application moves downward, the inclined pullout capacity increases, reaches its peak, and then starts to decrease.

Meso-Mechanics Analysis of Concrete: Generation of Random Aggregate Structure

2008 ◽  
Vol 400-402 ◽  
pp. 363-370
Author(s):  
Shao Fei Jiang ◽  
Zhao Qi Wu ◽  
Yun Fei Qiu
Keyword(s):  
Random Sampling ◽  
Progressive Failure ◽  
Aggregate Structure ◽  
Numerical Examples ◽  
Random Aggregate ◽  
Mechanics Analysis ◽  
Statistical Sense ◽  
Controlling Measures ◽  
External Loads ◽  
Aggregate Particles

In this paper, a new analytical method is proposed to generate concrete random aggregate structure (RAS) in meso-scopic level. This method is particular useful for the progressive failure of concrete under various external loads. In the meso-mechanics level, the concrete is taken as the composite material consisting of aggregate, mortar and interface between them. As a result, it is generated a random aggregate structure in which the shape, size and distribution of the aggregate particles resemble real concrete in the statistical sense using the Monte Carlo random sampling principle in this paper, and the method proposed can generate both regular aggregate particles and irregular ones in 2-Dimmension. It is should be noted that vector concept and some controlling measures are also proposed to avoid generating aggregate particles not consistent with real ones. Numerical examples are simulated to validate the proposed method finally.

Predicting the Benefits of Topology Optimization

2015 ◽  
Author(s):  
Shiguang Deng ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Shape Optimization ◽  
Systematic Method ◽  
Topological Sensitivity ◽  
Numerical Examples ◽  
Initial Design

Topology optimization is a systematic method of generating designs that maximize specific objectives. While it offers significant benefits over traditional shape optimization, topology optimization can be computationally demanding and laborious. Even a simple 3D compliance optimization can take several hours. Further, the optimized topology must typically be manually interpreted and translated into a CAD-friendly and manufacturing friendly design. This poses a predicament: given an initial design, should one optimize its topology? In this paper, we propose a simple metric for predicting the benefits of topology optimization. The metric is derived by exploiting the concept of topological sensitivity, and is computed via a finite element swapping method. The efficacy of the metric is illustrated through numerical examples.

A New Load Application System for In Vitro Study of Ligamentous Injuries to the Human Knee Joint

1995 ◽  
Vol 117 (4) ◽  
pp. 373-382 ◽  
Author(s):  
J. M. Bach ◽  
M. L. Hull
Keyword(s):  
Knee Joint ◽  
Degree Of Freedom ◽  
Load Application ◽  
Accuracy Evaluation ◽  
Application System ◽  
Human Knee ◽  
Human Knee Joint ◽  
Flexion Extension ◽  
External Loads

This paper describes the design and accuracy evaluation of a new six degree of freedom load application system for in vitro testing of the human knee joint. External loads of both polarity in all six degrees of freedom can be applied either individually or in any combination while the knee is permitted to move unconstrained in response to applied loads. The flexion/extension degree of freedom permits the full physiological range of motion. In addition to external loads, forces of the three major muscle groups (quadriceps, hamstrings, gastrocnemius) crossing the joint can be developed. Full automation and rapid convergence of loads to programmed values are achieved through a computer which feeds command signals to servo controller/electro-pneumatic servo valves. The servo valves regulate pressure to pneumatic actuators which develop the various loads. Experiments undertaken to quantify the accuracy of both load and displacement measurements reveal that errors particularly in load measurement are effectively controlled through the apparatus design.

Improvement of a topological level-set approach to find optimal topology by considering body forces

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Meisam Takalloozadeh ◽  
Gil Ho Yoon
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Thermal Loading ◽  
Topological Derivative ◽  
Optimization Process ◽  
Optimal Topology ◽  
Content Type ◽  
Body Forces ◽  
Applied Forces ◽  
Level Set Approach

Purpose Body forces are always applied to structures in the form of the weight of materials. In some cases, they can be neglected in comparison with other applied forces. Nevertheless, there is a wide range of structures in civil and mechanical engineering in which weight or other types of body forces are the main portions of the applied loads. The optimal topology of these structures is investigated in this study. Design/methodology/approach Topology optimization plays an increasingly important role in structural design. In this study, the topological derivative under body forces is used in a level-set-based topology optimization method. Instability during the optimization process is addressed, and a heuristic solution is proposed to overcome the challenge. Moreover, body forces in combination with thermal loading are investigated in this study. Findings Body forces are design-dependent loads that usually add complexity to the optimization process. Some problems have already been addressed in density-based topology optimization methods. In the present study, the body forces in a topological level-set approach are investigated. This paper finds that the used topological derivative is a flat field that causes some instabilities in the optimization process. The main novelty of this study is a technique used to overcome this challenge by using a weighted combination. Originality/value There is a lack of studies on level-set approaches that account for design-dependent body forces and the proposed method helps to understand the challenges posed in such methods. A powerful level-set-based approach is used for this purpose. Several examples are provided to illustrate the efficiency of this method. Moreover, the results show the effect of body forces and thermal loading on the optimal layout of the structures.

Simultaneous Shape and Topology Optimization of Planar Linkage Mechanisms Based on the Spring-Connected Rigid Block Model

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jeonghan Yu ◽  
Sang Min Han ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Simultaneous Optimization ◽  
Optimization Process ◽  
Rigid Block ◽  
Low Resolution ◽  
Block Model ◽  
Shape And Topology Optimization ◽  
Fixed Grid ◽  
Computation Efficiency ◽  
And Topology

Abstract Using the topology optimization can be an effective means of synthesizing planar rigid-body linkage mechanisms to generate desired motion, as it does not require a baseline mechanism for a specific topology. While most earlier studies were mainly concerned with the formulation and implementation of topology optimization-based synthesis in a fixed grid, this study aims to realize the simultaneous shape and topology optimization of planar linkage mechanisms using a low-resolution spring-connected rigid block model. Here, we demonstrate the effectiveness of simultaneous optimization over a higher-resolution fixed-grid rigid block-based topology optimization process. When shape optimization to change the block shapes is combined with topology optimization to synthesize the mechanism, the use of low-resolution discretized models improves the computation efficiency considerably and helps to yield compact mechanisms with less complexity, making them more amenable to fabrication. After verifying the effectiveness of the simultaneous shape and topology optimization process with several benchmark problems, we apply the method to synthesize a mechanism which guides a planar version of a human's gait trajectory.

Tracing Pareto-Optimal Frontiers in Topology Optimization

2010 ◽  
Author(s):  
Krishnan Suresh
Keyword(s):  
Fixed Point ◽  
Topology Optimization ◽  
Iteration Scheme ◽  
Stochastic Method ◽  
Pareto Optimal ◽  
Topological Sensitivity ◽  
Fixed Point Iteration ◽  
Numerical Examples ◽  
Multi Objective ◽  
Sensitivity Field

In multi-objective topology optimization, a design is defined to be “pareto-optimal” if no other design exists that is better with respect to one objective, and as good with respect to others. This unfortunately suggests that unless other ‘better’ designs are found, one cannot declare a particular topology to be pareto-optimal. In this paper, we first show that a topology can be guaranteed to be (locally) pareto-optimal if certain inherent properties associated with the topological sensitivity field are satisfied, i.e., no further comparison is necessary. This, in turn, leads to a deterministic, i.e., non-stochastic, method for directly tracing pareto-optimal frontiers using the classic fixed-point iteration scheme. The proposed method can generate the full set of pareto-optimal topologies in a single-run, and is therefore both efficient and predictable, as illustrated through numerical examples.

scholarly journals Geometric shape features extraction using a steady state partial differential equation system

2019 ◽  
Vol 6 (4) ◽  
pp. 647-656 ◽  
Author(s):  
Takayuki Yamada
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Analytical Solution ◽  
Geometric Shape ◽  
Geometrical Shape ◽  
Shape Features ◽  
Partial Differential ◽  
Topological Constraint ◽  
Numerical Examples

Abstract A unified method for extracting geometric shape features from binary image data using a steady-state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the thickness, orientation, and skeleton simultaneously. The main advantage of the proposed method is that the orientation is defined without derivatives and thickness computation is not imposed a topological constraint on the target shape. A one-dimensional analytical solution is provided to validate the proposed method. In addition, two-dimensional numerical examples are presented to confirm the usefulness of the proposed method. Highlights A steady state partial differential equation for extraction of geometrical shape features is formulated. The functions for geometrical shape features are formulated by the solution of the proposed PDE. Analytical solution is provided in one-dimension. Numerical examples are provided in two-dimension.

An Adaptive Continuation Method for Topology Optimization of Continuum Structures Considering Buckling Constraints

2017 ◽  
Vol 09 (07) ◽  
pp. 1750092 ◽  
Author(s):  
Xingjun Gao ◽  
Lijuan Li ◽  
Haitao Ma
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Continuation Method ◽  
Optimization Process ◽  
Continuum Structures ◽  
Design Evolution ◽  
Buckling Constraints ◽  
Load Factors ◽  
Structural Compliance ◽  
Parameter Values

This paper presents an adaptive continuation method for buckling topology optimization of continuum structures using the Solid Isotropic Material with Penalization (SIMP) model. For optimization problems of minimizing structural compliance subject to constraints on material volume and buckling load factors, it has been found that the conflict between the requirements for structural stiffness and stability may have an adverse impact on the performance of existing optimization algorithms. An automatic scheme for adjusting the penalization parameter is introduced to deal with this conflict and thus achieves better designs. Based on an investigation on the effect of the penalization parameter on design evolution during the optimization process, a rule is established to determine the appropriate penalization parameter values. Using this rule, an effective scheme is developed for determining the penalization parameter values such that the buckling constraints are appropriately considered throughout the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document