Trefftz- type FEM for solving orthotropic potential problems

Wang, K.Y.; Li, Peichao; Wang, D.Z.

doi:10.1590/s1679-78252014001400001

Cited by 15 publications

(7 citation statements)

References 31 publications

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“…As for the transformation-induced back-stress, it is usually not accounted for in the numerous crystal plasticity simulations of HCP found in the literature, such as the visco-plastic effective medium (mean-field) formulations [6], elasto-viscoplastic effective medium formulations [9,38], or full-field elasto-viscoplastic formulations [26][27]39]. Those models treat twinning as a pseudo-slip mechanism, which accommodates shear uniformly across the grain or across the corresponding finite element.…”

Section: 2twin Front Terminating At Grain Boundarymentioning

confidence: 99%

Numerical study of the stress state of a deformation twin in magnesium

et al. 2015

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We present here a numerical study of the distribution of local stress state associated with deformation twinning in Mg, both inside the twinned domain and in its immediate neighborhood, due to the accommodation of the twinning transformation shear. A full-field elasto-viscoplastic formulation based on Fast Fourier Transformation (FFT) is modified to include the shear transformation strain associated with deformation twinning. We have performed two types of twinning transformation simulations with: (i) the twin completely embedded inside a single crystal, and (ii) the twin front terminating at a grain boundary. We show that: (a) the resulting stress distribution is more strongly determined by the shear transformation than by the intragranular character of the twin or the orientation of the neighboring grain; (b) the resolved shear stress on the twin plane along the twin direction is inhomogeneous along the twin-parent interface; and (c) there are substantial differences in the average values of the shear stress in the twin and in the parent grain that contains the twin. We discuss the effect of these local stresses on twin propagation and growth, and the implications of our findings for the modeling of deformation twinning.

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Section: 2twin Front Terminating At Grain Boundarymentioning

confidence: 99%

Numerical study of the stress state of a deformation twin in magnesium

et al. 2015

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Section: Intelligent Topological Mmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wave Manipulation in Intelligent Metamaterials: Recent Progress and Prospects

Wu,

Jiang,

Jiang

et al. 2024

Adv Funct Materials

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Metamaterials (MMs), which include phononic crystals (PCs) as a particular type, exhibit anomalous wave propagation properties through artificial design of topologies or lattice forms of unit‐cells. Recent advancements in MMs signify an ascendant research trend, providing promising design ideas and means for unprecedented wave propagation properties. The imperative for on‐demand, real‐time active control of wave propagation underscores the significance of tunable manipulation of acoustic/elastic waves, promoting the design and development of tunable MMs. Furthermore, the versatility of intelligent materials and their ongoing development and innovation contribute significantly to the emergence of diverse intelligent MMs. This comprehensive survey provides an overview of recent advancements and current research trends in the interdisciplinary field of intelligent MMs with electro‐/magneto‐mechanical couplings. The primary objective of the review is to emphasize significant progress in agile manipulation of acoustic/elastic waves in electro‐/magneto‐mechanical coupled MMs, followed by an in‐depth exploration of intelligent metasurfaces, topological MMs, non‐Hermitian parity‐time symmetric wave systems, odd elastic MMs, and spatiotemporally modulated MMs. Special emphasis is given to multi‐field coupling effects. The review concludes with a summary and outlines potential prospects, offering a timely and informative guide for future studies on actively tunable PCs and MMs in practical engineering applications.

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“…The paper [12] considers the analysis of vibrations and stability of thick orthotropic plates using finite elements based on the Treffz hybrid formula. The Treffz type finite element method (TFEM) is used by C. Young [13] to solve some potential problems in orthotropic environment. The method of boundary elements in classical form was used in [14].…”

Section: Latest Researches Analysismentioning

confidence: 99%

Stability of orthotropic plates

2020

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The solution to the problem of the stability of a rectangular orthotropic plate is described by the numerical-analytical method of boundary elements. As is known, the basis of this method is the analytical construction of the fundamental system of solutions and Green's functions for the differential equation (or their system) for the problem under consideration. To account for certain boundary conditions, or contact conditions between the individual elements of the system, a small system of linear algebraic equations is compiled, which is then solved numerically. It is shown that four combinations of the roots of the characteristic equation corresponding to the differential equation of the problem are possible, which leads to the need to determine sixty-four analytical expressions of fundamental functions. The matrix of fundamental functions, which is the basis of the transcendental stability equation, is very sparse, which significantly improves the stability of numerical operations and ensures high accuracy of the results. An analysis of the numerical results obtained by the author's method shows very good convergence with the results of finite element analysis. For both variants of the boundary conditions, the discrepancy for the corresponding critical loads is almost the same, and increases slightly with increasing critical load. Moreover, this discrepancy does not exceed one percent. It is noted that under both variants of the boundary conditions, the critical loads calculated by the boundary element method are less than in the finite element calculations. The obtained transcendental stability equation allows to determine critical forces both by the static method and by the dynamic one. From this equation it is possible to obtain a spectrum of critical forces for a fixed number of half-waves in the direction of one of the coordinate axes. The proposed approach allows us to obtain a solution to the stability problem of an orthotropic plate under any homogeneous and inhomogeneous boundary conditions.

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Trefftz- type FEM for solving orthotropic potential problems

Cited by 15 publications

References 31 publications

Numerical study of the stress state of a deformation twin in magnesium

Numerical study of the stress state of a deformation twin in magnesium

Wave Manipulation in Intelligent Metamaterials: Recent Progress and Prospects

Stability of orthotropic plates

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