scholarly journals Comparative Study of Peridynamics and Finite Element Method for Practical Modeling of Defects Cracks in Topology Optimization

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1407
Author(s):  
Peyman Lahe Motlagh ◽  
Adnan Kefal
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Comparative Study ◽  
Strain Energy ◽  
Optimality Criteria ◽  
Design Stage ◽  
Design Domain ◽  
Optimum Topology ◽  
Strain Stress

Recently, topology optimization of structures with cracks becomes an important topic for avoiding manufacturing defects at the design stage. This paper presents a comprehensive comparative study of peridynamics-based topology optimization method (PD-TO) and classical finite element topology optimization approach (FEM-TO) for designing lightweight structures with/without cracks. Peridynamics (PD) is a robust and accurate non-local theory that can overcome various difficulties of classical continuum mechanics for dealing with crack modeling and its propagation analysis. To implement the PD-TO in this study, bond-based approach is coupled with optimality criteria method. This methodology is applicable to topology optimization of structures with any symmetric/asymmetric distribution of cracks under general boundary conditions. For comparison, optimality criteria approach is also employed in the FEM-TO process, and then topology optimization of four different structures with/without cracks are investigated. After that, strain energy and displacement results are compared between PD-TO and FEM-TO methods. For design domain without cracks, it is observed that PD and FEM algorithms provide very close optimum topologies with a negligibly small percent difference in the results. After this validation step, each case study is solved by integrating the cracks in the design domain as well. According to the simulation results, PD-TO always provides a lower strain energy than FEM-TO for optimum topology of cracked structures. In addition, the PD-TO methodology ensures a better design of stiffer supports in the areas of cracks as compared to FEM-TO. Furthermore, in the final case study, an intended crack with a symmetrically designed size and location is embedded in the design domain to minimize the strain energy of optimum topology through PD-TO analysis. It is demonstrated that hot-spot strain/stress regions of the pristine structure are the most effective areas to locate the designed cracks for effective redistribution of strain/stress during topology optimization.

Topology Optimization Using Node-Based Smoothed Finite Element Method

2015 ◽  
Vol 07 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Z. C. He ◽  
G. Y. Zhang ◽  
L. Deng ◽  
Eric Li ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Optimization Design ◽  
Solid Mechanics ◽  
Optimality Criteria ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Smoothed Finite Element Method ◽  
Element Method

The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.

Solving Downslope Pipeline Walking on Non-Linear Soil With Brittle Peak Strength and Strain Softening

2017 ◽  
Author(s):  
Adriano Castelo ◽  
David White ◽  
Yinghui Tian
Keyword(s):  
Finite Element ◽  
Strain Softening ◽  
Peak Strength ◽  
Design Stage ◽  
Rigid Plastic ◽  
Soil Model ◽  
Interaction Behavior ◽  
Study Results ◽  
Non Linear

In 2000 the first case of pipeline walking (PW) was properly documented when this phenomenon seriously impacted a North Sea high pressure and high temperature (HP/HT) pipeline (Tornes et al. 2000). By then, the main drivers of this problem were accordingly identified for the case studied. On the other hand, to study other aspects related not only to PW, the industry joined forces in the SAFEBUCK Joint Industry Project (JIP) with academic partners. As a result, other drivers, which lead a pipeline to walk, have been identified (Bruton et al. 2010). Nowadays, during the design stage of pipelines, estimates are calculated for pipeline walking. These estimates often use a Rigid-Plastic (RP) soil idealization and the Coulomb friction principle (Carr et al. 2006). Unfortunately, this model does not reflect the real pipe-soil interaction behavior, and in practice time consuming finite element computations are often performed using an Elastic-Perfectly-Plastic (EPP) soil model. In reality, some observed axial pipe-soil responses are extremely non-linear and present a brittle peak strength before a strain softening response (White et al. 2011). This inaccuracy of the soil representation normally overestimates the Walking Rate (WR) (a rigid plastic soil model leads to greater walking). A magnified WR invariably leads to false interpretations besides being unrealistic. Finally, a distorted WR might also demand mitigating measures that could be avoided if the soil had been adequately treated. Unnecessary mitigation has a very strong and negative effect on the project as whole. It will require more financial and time investments for the entire development of the project — from design to construction activities. Therefore, having more realistic and pertinent estimates becomes valuable not only because of budgetary issues but also because of time frame limits. The present paper will show the results of a set of Finite Element Analyses (FEA) performed for a case-study pipeline. The analyses — carried out on ABAQUS software — used a specific subroutine code prepared to appropriately mimic Non-Linear Brittle Peak with Strain Softening (NLBPSS) axial pipe-soil interaction behavior. The specific subroutine code was represented in the Finite Element Models (FEMs) by a series of User Elements (UELs) attached to the pipe elements. The NLBPSS case is a late and exclusive contribution from the present work to the family of available pipeline walking solutions for different forms of axial pipe-soil interaction model. The parametric case-study results are benchmarked against theoretical calculations of pipeline walking showing that the case study results deliver a reasonable accuracy level and are reliable. The results are then distilled into a simplified method in which the WR for NLBPSS soil can be estimated by adjusting a solution derived for RP and EPP soil. The key outcome is a genuine method to correct the WR resultant from a RP soil approach to allow for peak and softening behaviour. It provides a design tool that extends beyond the previously-available solutions and allows more rapid and efficient predictions of pipeline walking to be made. This contribution clarifies, for the downslope walking case, what is the most appropriate basis to incorporate or idealize the soil characteristics within the axial Pipe-Soil Interaction (PSI) response when performing PW assessments.

Application of Regional Strain Energy in Topology Optimization With Inertia Relief Analysis

2013 ◽  
Author(s):  
Wei Song ◽  
Hae Chang Gea ◽  
Ren-Jye Yang ◽  
Ching-Hung Chuang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Strain Energy ◽  
Computational Cost ◽  
Structure Design ◽  
Protective Structure ◽  
Element Analysis ◽  
Regional Strain ◽  
Unbalanced Loads ◽  
Energy Formulation

In finite element analysis, inertia relief solves the response of an unconstrained structure subject to constant or slowly varying external loads with static analysis computational cost. It is very attractive to utilize it in topology optimization to design structures under unbalanced loads, such as in impact and drop phenomena. In this paper, regional strain energy formulation and inertia relief is integrated into topology optimization to design protective structure under unbalanced loads. For background, the equations of inertia relief are introduced and a commonly used solving method is revisited. Then the regional strain energy formulation for topology optimization with inertia relief is proposed and its sensitivity is derived from the adjoint method. Based on the solving method, the sensitivity is evaluated term by term to simplify the results. The simplified sensitivity can be calculated easily using the output of commercial finite element packages. Finally, the effectiveness of this formulation is shown in the first example and the proposed regional strain energy formulation for topology optimization with inertia relief are presented and discussed in the protective structure design examples.

Topology Optimization With Multiple Constraints

1995 ◽  
Author(s):  
R. J. Yang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Optimality Criteria ◽  
Topology Design ◽  
Structural Components ◽  
Material Density ◽  
Structural Responses ◽  
Mathematical Programming Method ◽  
General Optimization Problem

Abstract Topology optimization is used for determining the best layout of structural components to achieve predetermined performance goals. The density method which uses material density of each finite element as the design variable is employed. Unlike the most common approach which uses the optimality criteria methods, the topology design problem is formulated as a general optimization problem and is solved by the mathematical programming method. One of the major advantages of this approach is its generality; thus it can solve various problems, e.g. multi-objective and multi-constraint problems. In this study, the structural weight is chosen as the objective function and structural responses such as the compliances, displacements, and the natural frequencies are treated as the constraints. The MSC/NASTRAN finite element code is employed for response analyses. One example with four different optimization formulations was used to demonstrate this approach.

Multistage topology optimization of induction heating apparatus in time domain electromagnetic field with magnetic nonlinearity

2019 ◽  
Vol 38 (3) ◽  
pp. 1009-1022
Author(s):  
Hiroshi Masuda ◽  
Yoshifumi Okamoto ◽  
Shinji Wakao
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Induction Heating ◽  
Time Domain ◽  
Computation Time ◽  
Design Domain ◽  
Element Mesh ◽  
Content Type ◽  
Actual Application ◽  
Application Model

Purpose The purpose of this paper is to solve efficiently the topology optimization (TO) in time domain problem with magnetic nonlinearity requiring a large-scale finite element mesh. As an actual application model, the proposed method is applied to induction heating apparatus. Design/methodology/approach To achieve TO with efficient computation time, a multistage topology is proposed. This method can derive the optimum structure by repeatedly reducing the design domain and regenerating the finite element mesh. Findings It was clarified that the structure derived from proposed method can be similar to the structure derived from the conventional method, and that the computation time can be made more efficient by parameter tuning of the frequency and volume constraint value. In addition, as a time domain induction heating apparatus problem of an actual application model, an optimum topology considering magnetic nonlinearity was derived from the proposed method. Originality/value Whereas the entire design domain must be filled with small triangles in the conventional TO method, the proposed method requires finer mesh division of only the stepwise-reduced design domain. Therefore, the mesh scale is reduced, and there is a possibility that the computation time for TO can be shortened.

Concurrent Topology Optimization of Lightweight Cellular Materials and Structures

2017 ◽  
Vol 868 ◽  
pp. 291-296
Author(s):  
He Ting Qiao ◽  
Shi Jie Wang ◽  
Xiao Ren Lv
Keyword(s):  
Topology Optimization ◽  
Material Design ◽  
Cellular Materials ◽  
Cellular Material ◽  
Design Stage ◽  
Concurrent Design ◽  
Design Variables ◽  
Macro Scale ◽  
Optimum Topology ◽  
Two Stages

In this paper, a two-stage optimization algorithm is proposed to simultaneously achieve the optimum structure and microstructure of lightweight cellular materials. Microstructure is assumed being uniform in macro-scale to meet manufacturing requirements. Furthermore, to reduce the computation cost, the design process is divided into two stages, which are concurrent design and material design. In the first stage, macro density and modulus matrix of cellular material are used both as design variables. Then, the optimum topology of macro-structure and modulus matrix of cellular materials will be obtained under this configuration. In the second stage, topology optimization technology is used to achieve a micro-structure of cellular material which is corresponded with the optimum modulus matrix in the earlier concurrent design stage. Moreover, the effectiveness of the present design methodology and optimization scheme is then demonstrated through numerical example.

A Review of Methods to Characterize Rubber Elastic Behavior for Use in Finite Element Analysis

1994 ◽  
Vol 67 (3) ◽  
pp. 481-503 ◽  
Author(s):  
D. J. Charlton ◽  
J. Yang ◽  
K. K. Teh
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Physical Testing ◽  
Synthetic Test ◽  
Elastic Strain Energy Density

Abstract The purpose of this paper is to provide a review of methods used to characterize the elastic behavior of rubber for use in Finite Element Analysis (FEA). A sample of elastic strain energy density functions used to characterize rubber is given, along with the tests required to characterize rubber according to these functions. The use of synthetic test data as an alternative to full physical testing is discussed, and highlighted by a case study. The paper closes with a discussion on potential errors associated with FEA of rubber components.

scholarly journals TOMARES

2021 ◽  
Author(s):  
Laura Malena Lottes ◽  
Nils Kaiser ◽  
Nils Goossens ◽  
Holger W. Oelze ◽  
Claus Braxmaier
Keyword(s):  
Finite Element ◽  
Angular Momentum ◽  
Topology Optimization ◽  
Energy Density ◽  
Design Space ◽  
Aerospace Industry ◽  
Reaction Wheel ◽  
Expected Performance ◽  
Payload Mass

AbstractIn aerospace industry, saving mass on spacecrafts always remain in large demand to save launch costs or increase the available payload mass. A case study is carried out designing a first concept of an additive manufactured flywheel of a reaction wheel, as it is one of the heaviest parts of wheel systems. As an objective the mass is minimized, while obtaining an angular momentum suitable according to mission requirements and maintaining recent performances. As references the SeaSAT mission and a commercial reaction wheel are used. The work includes a preliminary dimension of the flywheels design space by MATLAB calculations, where in total 15 shapes are analyzed and compared. The most promising design space is afterwards analyzed via the finite-element tool ANSYS and is defined as the reference flywheel. The reference flywheel is used for topology optimizations (ANSYS Topology Optimization), where different boundary conditions are considered. The final designed flywheel obtains 16% higher energy density than the reference flywheel and withstands the mission loads. It can be concluded that it was possible to design a flywheel obtaining less mass while keeping the expected performance.

scholarly journals A Comparative Study of the Application of Different Commercial Software for Topology Optimization

2022 ◽  
Vol 12 (2) ◽  
pp. 611
Author(s):  
Evangelos Tyflopoulos ◽  
Martin Steinert
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Design Method ◽  
Design Domain ◽  
Online Database ◽  
Objective Functions ◽  
Commercial Software ◽  
Optimization Software ◽  
Software Platforms ◽  
The Given

Topology optimization (TO) has been a popular design method among CAD designers in the last decades. This method optimizes the given design domain by minimizing/maximizing one or more objective functions, such as the structure’s stiffness, and at the same time, respecting the given constraints like the volume or the weight reduction. For this reason, the companies providing the commercial CAD/FEM platforms have taken this design trend into account and, thus, have included TO in their products over the last years. However, it is not clear which features, algorithms, or, in other words, possibilities the CAD designers do have using these software platforms. A comparative study among the most applied topology optimization software was conducted for this research paper. First, the authors developed an online database of the identified TO software in the form of a table. Interested CAD designers can access and edit its content, contributing in this way to the creation of an updated library of the available TO software. In addition, a deeper comparison among three commercial software platforms—SolidWorks, ANSYS Mechanical, and ABAQUS—was implemented using three common case studies—(1) a bell crank lever, (2) a pillow bracket, and (3) a small bridge. These models were designed, optimized, and validated numerically, as well as compared for their strength. Finally, the above software was evaluated with respect to optimization time, optimized designs, and TO possibilities and features.

The Influence of Blind-Hole Depth and Bore to Strain Energy Relief Coefficients-a Case Study

2012 ◽  
Vol 479-481 ◽  
pp. 1993-1996
Author(s):  
Xiao Hong Liu ◽  
Chang Qing Guo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strain Energy ◽  
Measurement Accuracy ◽  
Stress And Strain ◽  
Hole Depth ◽  
Blind Hole ◽  
Hole Edge ◽  
Improve Measurement

In order to improve measurement accuracy and for choosing the best ratio of hole depth to bore (h/d), a model based on 16Mn was setup for studying the influence of different hole depth h and bore d to the coefficients with finite element method (FEM). The stress and strain on hole edge was simulated and the influence of h/d to the strain relief coefficient A, B were studied. By applying different loads, the relation of A, B vs. stress σ was studied under the conditions of σ=1/3σs. The results showed that more accurate coefficients were achieved when h/d was set to 1.25.

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