Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions

2006 ◽  
Vol 32 (3) ◽  
pp. 229-240 ◽  
Author(s):  
E. A. Fancello
Keyword(s):  
Topology Optimization ◽  
Boundary Conditions ◽  
Local Failure ◽  
Contact Boundary ◽  
Minimum Mass

scholarly journals TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain

2020 ◽  
Author(s):  
Zhenguo Nie ◽  
Tong Lin ◽  
Haoliang Jiang ◽  
Levent Burak Kara
Keyword(s):  
Topology Optimization ◽  
Boundary Conditions ◽  
Mean Squared Error ◽  
Sparse Matrices ◽  
Hybrid Network ◽  
Generative Adversarial Networks ◽  
Test Problems ◽  
Generative Adversarial Network ◽  
The Mean ◽  
Physical Fields

Abstract In topology optimization using deep learning, load and boundary conditions represented as vectors or sparse matrices often miss the opportunity to encode a rich view of the design problem, leading to less than ideal generalization results. We propose a new data-driven topology optimization model called TopologyGAN that takes advantage of various physical fields computed on the original, unoptimized material domain, as inputs to the generator of a conditional generative adversarial network (cGAN). Compared to a baseline cGAN, TopologyGAN achieves a nearly 3× reduction in the mean squared error and a 2.5× reduction in the mean absolute error on test problems involving previously unseen boundary conditions. Built on several existing network models, we also introduce a hybrid network called U-SE(Squeeze-and-Excitation)-ResNet for the generator that further increases the overall accuracy. We publicly share our full implementation and trained network.

Checking the Automated Construction of Finite Element Simulations From Dirichlet Boundary Conditions

2019 ◽  
Author(s):  
Kevin N. Chiu ◽  
Mark D. Fuge
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Fem Simulation ◽  
Computational Design ◽  
Dirichlet Boundary Conditions ◽  
Governing Equations ◽  
Variational Form ◽  
Key Issues

Abstract From engineering analysis and topology optimization to generative design and machine learning, many modern computational design approaches require either large amounts of data or a method to generate that data. This paper addresses key issues with automatically generating such data through automating the construction of Finite Element Method (FEM) simulations from Dirichlet boundary conditions. Most past work on automating FEM assumes prior knowledge of the physics to be run or is limited to a small number of governing equations. In contrast, we propose three improvements to current methods of automating the FEM: (1) completeness labels that guarantee viability of a simulation under specific conditions, (2) type-based labels for solution fields that robustly generate and identify solution fields, and (3) type-based labels for variational forms of governing equations that map the three components of a simulation set — specifically, boundary conditions, solution fields, and a variational form — to each other to form a viable FEM simulation. We implement these improvements using the FEniCS library as an example case. We show that our improvements increase the percent of viable simulations that are run automatically from a given list of boundary conditions. This paper’s procedures ultimately allow for the automatic — i.e., fully computer-controlled — construction of FEM multi-physics simulations and data collection required to run data-driven models of physics phenomena or automate the exploration of topology optimization under many physics.

scholarly journals Brain–skull contact boundary conditions in an inverse computational deformation model

2009 ◽  
Vol 13 (4) ◽  
pp. 659-672 ◽  
Author(s):  
Songbai Ji ◽  
David W. Roberts ◽  
Alex Hartov ◽  
Keith D. Paulsen
Keyword(s):  
Boundary Conditions ◽  
Contact Boundary ◽  
Deformation Model

A Penetration-Based Finite Element Method for Hyperelastic 3D Biphasic Tissues in Contact: Part 1-Derivation of Contact Boundary Conditions

2005 ◽  
Vol 128 (1) ◽  
pp. 124-130 ◽  
Author(s):  
Kerem Ün ◽  
Robert L. Spilker
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Contact Boundary ◽  
Element Analysis ◽  
Efficient Manner ◽  
Biphasic Tissues ◽  
Element Method

In this study, we extend the penetration method, previously introduced to simulate contact of linear hydrated tissues in an efficient manner with the finite element method, to problems of nonlinear biphasic tissues in contact. This paper presents the derivation of contact boundary conditions for a biphasic tissue with hyperelastic solid phase using experimental kinematics data. Validation of the method for calculating these boundary conditions is demonstrated using a canonical biphasic contact problem. The method is then demonstrated on a shoulder joint model with contacting humerus and glenoid tissues. In both the canonical and shoulder examples, the resulting boundary conditions are found to satisfy the kinetic continuity requirements of biphasic contact. These boundary conditions represent input to a three-dimensional nonlinear biphasic finite element analysis; details of that finite element analysis will be presented in a manuscript to follow.

Efficient Design of Lightweight Reinforced Tensegrities Under Local and Global Failure Constraints

2020 ◽  
Vol 87 (11) ◽  
Author(s):  
Raman Goyal ◽  
Robert E. Skelton ◽  
Edwin A. Peraza Hernandez
Keyword(s):  
External Force ◽  
Design Method ◽  
Numerical Approach ◽  
Dominant Mode ◽  
Local Failure ◽  
Mode Shapes ◽  
Minimum Mass ◽  
Efficient Design ◽  
Global Buckling ◽  
External Forces

Abstract Tensegrities are prestressable trusses that have been proven to support various load distributions with minimum mass. This article presents a novel efficient method for designing lightweight tensegrities under local and global failure constraints. Local failure includes buckling and material yielding of individual members in the tensegrity. Global failure refers to global buckling of the tensegrity, where it loses stability without undergoing local failure at its individual members. The formulation and numerical approach to determine the critical global buckling forces and mode shapes of tensegrities with arbitrary shape and topology are first provided. Next, the design method considering local and global failure is presented, which starts with the local sizing of the member areas of the given tensegrity for the prevention of local failure. The method then determines the dominant failure mode by comparing the external forces and the critical global buckling force of the locally sized structure. If the critical global buckling force is larger than the external force, the dominant mode is a local failure and the locally sized design is returned as the minimum mass design. Conversely, if global failure is the dominant mode, different global reinforcement approaches are applied to raise the critical buckling force of the structure until it matches the external force, preventing global buckling. These reinforcement approaches include increasing the areas of the members and increasing the prestress in the tensegrity. Representative examples are provided to demonstrate the effectiveness of the design method considering box and T-bar tensegrities.

An Evaluation of Three-Dimensional Diarthrodial Joint Contact Using Penetration Data and the Finite Element Method

2001 ◽  
Vol 123 (4) ◽  
pp. 333-340 ◽  
Author(s):  
W. L. Dunbar, ◽  
K. U¨n ◽  
P. S. Donzelli ◽  
R. L. Spilker
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Contact Boundary ◽  
Element Analysis ◽  
Joint Contact ◽  
Three Dimensional Finite Element

We have developed an approximate method for simulating the three-dimensional contact of soft biphasic tissues in diarthrodial joints under physiological loading. Input to the method includes: (i) kinematic information describing an in vitro joint articulation, measured while the cartilage is deformed under physiological loads, (ii) geometric properties for the relaxed (undeformed) cartilage layers, obtained for the analyses in this study via stereophotogrammetry, and (iii) material parameters for the biphasic constitutive relations used to represent cartilage. Solid models of the relaxed tissue layers are assembled in physiological positions, resulting in a mathematical overlap of the cartilage layers. The overlap distribution is quantified and converted via the biphasic governing equations into applied traction boundary conditions for both the solid and fluid phases for each of the contacting layers. Linear, biphasic, three-dimensional, finite element analysis is performed using the contact boundary conditions derived for each of the contacting layers. The method is found to produce results consistent with the continuity requirements of biphasic contact. Comparison with results from independent, biphasic contact analyses of axisymmetric problems shows that the method slightly underestimates the contact area, leading to an overestimation of the total traction, but yields a good approximation to elastic stress and solid phase displacement.

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