AI-Timoshenko: Automatedly Discovering Simplified Governing Equations for Applied Mechanics Problems from Simulated Data

2021 ◽  
pp. 1-37
Author(s):  
Zhanchao Huang ◽  
Chunjiang Li ◽  
Z. L. Huang ◽  
Yong Wang ◽  
Hanqing Jiang
Keyword(s):  
Finite Element Method ◽  
Simulated Data ◽  
Data Driven ◽  
Trial And Error ◽  
Applied Mechanics ◽  
Governing Equations ◽  
Displacement Fields ◽  
3D Finite Element ◽  
3D Finite Element Method ◽  
Beam Theories

Abstract The simplified governing equations of applied mechanics play a pivotal role and were derived based on ingenious assumptions or hypotheses regarding the displacement fields for specific problems. In this paper, we introduce a data-driven method by the name AI-Timoshenko in honor of Timoshenko, father of applied mechanics, to automatically discover simplified governing equations for applied mechanics problems directly from discrete data simulated by the 3D finite element method. This liberates applied mechanicians from burdensome labor, including assumptions, derivation, and trial and error. The simplified governing equations for Euler-Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems.

Bending Analysis of SMA Embedded Rectangular Laminated Sandwich Plates with Soft Core Using 3D Finite Element Method

2011 ◽  
Vol 110-116 ◽  
pp. 1458-1465 ◽  
Author(s):  
M. Khadem ◽  
M. M. Kheirikhah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transverse Shear ◽  
Soft Core ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
3D Finite Element ◽  
Bending Analysis ◽  
Transverse Shear Stresses ◽  
3D Finite Element Method

Nowadays Shape Memory Alloys (SMAs) are used as actuators in many applications such as aerospace structures. In sandwich structures, the SMA wires or plates are used in the skins for shape control of the structure or vibration damping. In this paper, bending behavior of sandwich plates with embedded SMA wires in their skins is studied. 3D finite element method is used for construction and analysis of the sandwich plate with a flexible core and two stiff skins. Some important points such as continuity conditions of the displacements, satisfaction of interlaminar transverse shear stresses, the conditions of zero transverse shear stresses on the upper and lower surfaces and in-plane and transverse flexibility of soft core are considered for accurate modeling and analysis of sandwich structures. Solution for bending analysis of sandwich plates under various transverse loads are presented and the effect of many parameters such as plate dimensions, loading conditions, material properties of core, skins and SMA wires are studied. Comparison of the present results in special case with those of the three-dimensional theory of elasticity and some plate theories confirms the accuracy of the proposed model.

scholarly journals Dry Friction Interblade Damping by 3D FEM Modelling of Bladed Disk: HPC Calculations Compared with Experiment

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Luděk Pešek ◽  
Pavel Šnábl ◽  
Vítězslav Bula
Keyword(s):  
Finite Element Method ◽  
Dry Friction ◽  
Computational Time ◽  
Friction Contact ◽  
3D Fem ◽  
3D Finite Element ◽  
Bladed Disk ◽  
3D Finite Element Method ◽  
Good Agreement ◽  
Damping Estimation

Interblade contacts and damping evaluation of the turbine bladed wheel with prestressed dry friction contacts are solved by the 3D finite element method with the surface-to-surface dry friction contact model. This makes it possible to model the space relative motions of contact pairs that occur during blade vibrations. To experimentally validate the model, a physical model of the bladed wheel with tie-boss couplings was built and tested. HPC computation with a proposed strategy was used to lower the computational time of the nonlinear solution of the wheel resonant attenuation used for damping estimation. Comparison of experimental and numerical results of damping estimation yields a very good agreement.

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