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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Sequence Networks of Rotating Machines01:24

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A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
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Joints, also known as articulations, are classified based on their structural characteristics, i.e., based on whether the articulating surfaces of the adjacent bones are directly connected by fibrous connective tissue or cartilage, or whether the articulating surfaces contact each other within a fluid-filled joint cavity. These differences serve to divide the joints of the body into three structural classifications.
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The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
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Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting
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Generative machine learning algorithm for lattice structures with superior mechanical properties.

Sangryun Lee1, Zhizhou Zhang1, Grace X Gu1

  • 1Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA. ggu@berkeley.edu.

Materials Horizons
|February 9, 2022
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Summary
This summary is machine-generated.

Engineers optimized lattice structure design using deep learning and Bézier curves. This novel approach enhances material distribution for superior strength and efficiency in load-bearing applications.

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Area of Science:

  • Mechanical Engineering
  • Materials Science
  • Computational Design

Background:

  • Lattice structures offer effective material distribution but face a density-mechanical property trade-off.
  • Uniform beam cross-sections in current designs limit optimization and weight-to-performance ratios.

Purpose of the Study:

  • To investigate optimized beam element shapes in lattice structures using advanced computational methods.
  • To explore an augmented design space for superior lattice structures with improved weight-to-performance ratios.

Main Methods:

  • Utilized a deep learning approach with high-order Bézier curves to define beam element shapes.
  • Employed a hybrid neural network and genetic optimization (NN-GO) adaptive method for lattice generation.
  • Fabricated optimized designs via additive manufacturing and validated through compression testing.

Main Results:

  • Optimized designs shifted material towards joints, enhancing modulus and strength.
  • Achieved a balance between axial and bending deformation modes for efficient load bearing and energy absorption.
  • Demonstrated superior performance over benchmark designs, with good correlation between simulations and experiments.

Conclusions:

  • High-order Bézier curves enable smoother transitions, reducing stress concentration in lattice structures.
  • The deep learning and NN-GO approach successfully generates high-performance lattice designs.
  • Optimized lattice structures show significant improvements in mechanical properties and efficiency.