scholarly journals A Novel Peridynamic Mindlin Plate Formulation Without Limitation on Material Constants

2021 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Strain Energy ◽  
Material Point ◽  
Mindlin Plate ◽  
Lagrange Equations ◽  
Element Analysis ◽  
Thick Plates ◽  
Material Constants ◽  
Simply Supported ◽  
Current Formulation ◽  
Different Types

AbstractIn this study, a new peridynamic Mindlin plate formulation is introduced by utilising Euler-Lagrange equations. The classical strain energy density of a material point is converted to its corresponding peridynamic form by using Taylor’s expansions. The formulation is suitable for thick plates by considering the transverse shear deformation. Material constants do not have any limitation in the current formulation. Different types of boundary conditions are considered in numerical examples including simply supported, clamped and mixed (clamped-supported). To verify the current formulation, peridynamic solutions of the transverse displacements and rotations are compared against solutions obtained from finite element analysis.

scholarly journals Peridynamic Mindlin Plate Formulation for Functionally Graded Materials

2020 ◽  
Vol 4 (2) ◽  
pp. 76
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Benchmark Problems ◽  
Lagrange Equations ◽  
Element Analysis ◽  
Graded Materials ◽  
Simply Supported ◽  
New Formulation ◽  
Good Agreement

In this study, a new peridynamic Mindlin plate formulation is presented which is suitable for the analysis of functionally graded materials. The governing equations of peridynamic formulation are obtained by using Euler-Lagrange equations in conjunction with Taylor’s expansion. To validate the new formulation, three different numerical benchmark problems are considered for a Mindlin plate subjected to simply supported, fully clamped and mixed (clamped-simply supported) boundary conditions. Peridynamic results are compared against results from finite element analysis and a good agreement is observed between the two methods.

scholarly journals New Analytic Free Vibration Solutions of Rectangular Thick Plates With a Free Corner by the Symplectic Superposition Method

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Rui Li ◽  
Pengcheng Wang ◽  
Bo Wang ◽  
Chunyu Zhao ◽  
Yewang Su
Keyword(s):  
Free Vibration ◽  
Analytic Solutions ◽  
The Other ◽  
Superposition Method ◽  
Element Analysis ◽  
Thick Plates ◽  
Simply Supported ◽  
Vibrating Plates ◽  
First Time ◽  
Mathematical Derivation

Seeking analytic free vibration solutions of rectangular thick plates without two parallel simply supported edges is of significance for an insight into the performances of related engineering devices and structures as well as their rapid design. A challenging set of problems concern the vibrating plates with a free corner, i.e., those with two adjacent edges free and the other two edges clamped or simply supported or one of them clamped and the other one simply supported. The main difficulty in solving one of such problems is to find a solution meeting both the boundary conditions at each edge and the condition at the free corner, which is unattainable using a conventional analytic method. In this paper, for the first time, we extend a novel symplectic superposition method to free vibration of rectangular thick plates with a free corner. The analytic frequency and mode shape solutions are both obtained and presented via comprehensive numerical and graphic results. The rigorousness in mathematical derivation and rationality of the method (without any predetermination for the solutions) guarantee the validity of our analytic solutions, which themselves are also validated by the reported results and refined finite element analysis.

ANSYS Simply Supported Deep Beams Based on the Study of Mechanical Properties

2013 ◽  
Vol 351-352 ◽  
pp. 782-785
Author(s):  
Yong Bing Liu ◽  
Xiao Zhong Zhang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Mechanical Model ◽  
Work Performance ◽  
Deep Beam ◽  
Analysis Software ◽  
Deep Beams ◽  
Element Analysis ◽  
Simply Supported ◽  
Force Characteristics

Established the mechanical model of simply supported deep beam, calculation and analysis of simple supported deep beams by using finite element analysis software ANSYS, simulated the force characteristics and work performance of the deep beam. Provides the reference for the design and construction of deep beams.

Column Moment Demands from Orthogonal Beam Twisting

2018 ◽  
Vol 763 ◽  
pp. 259-269
Author(s):  
George Webb ◽  
Kanyakon Kosinanonth ◽  
Tushar Chaudhari ◽  
Saeid Alizadeh ◽  
Gregory A. MacRae
Keyword(s):  
Lateral Displacement ◽  
Frame Structure ◽  
Moment Frames ◽  
Steel Moment Frames ◽  
Element Analysis ◽  
Soft Storey ◽  
Simply Supported ◽  
Composite Frame ◽  
Explicit Consideration ◽  
Column Joint

Beam column joint subassemblies in steel moment frames often have simply-supported gravity beams framing into the joint in the perpendicular direction. When these subassemblies undergo lateral displacement, moments enter the column from the beams. Some of these moments are directly applied from the in-plane beam and slab stresses as they contact the column, and additional moments occur as the slab causes the perpendicular simply supported beams to twist. In most design codes around the world, no explicit consideration of these moments is performed even though they may increase the likelihood of column yielding and a soft-storey mechanism. This paper quantifies the magnitude of these perpendicular beam twisting moments in typical subassemblies using inelastic finite element analysis. It is shown that for beam-column-joint-slab subassemblies where the primary and secondary beams are fully welded to the column, the addition of slab effects significantly increases the total stiffness and strength of the composite frame structure. In addition to this, it is also shown the twisting moment demand of the secondary beams increased the frames strength by approximately 2% for an imposed drift of 5% for the subassembly investigated when no gap was provided between slab and the column. It was also shown the twisting moment demand of the secondary beams increased the frames strength by approximately 10% for a maximum imposed drift of 5% for the subassembly investigated when a gap was provided between the slab and the column.

Vibration-Based Crack Detection in L-Frames

2014 ◽  
Vol 658 ◽  
pp. 261-268
Author(s):  
Jean Louis Ntakpe ◽  
Gilbert Rainer Gillich ◽  
Florian Muntean ◽  
Zeno Iosif Praisach ◽  
Peter Lorenz
Keyword(s):  
Strain Energy ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Structural Elements ◽  
Element Analysis ◽  
Accurate Localization ◽  
Mathematical Expressions ◽  
Measurement Results ◽  
Non Destructive

This paper presents a novel non-destructive method to locate and size damages in frame structures, performed by examining and interpreting changes in measured vibration response. The method bases on a relation, prior contrived by the authors, between the strain energy distribution in the structure for the transversal vibration modes and the modal changes (in terms of natural frequencies) due to damage. Using this relation a damage location indicator DLI was derived, which permits to locate cracks in spatial structures. In this paper an L-frame is considered for proving the applicability of this method. First the mathematical expressions for the modes shapes and their derivatives were determined and simulation result compared with that obtained by finite element analysis. Afterwards patterns characterizing damage locations were derived and compared with measurement results on the real structure; the DLI permitted accurate localization of any crack placed in the two structural elements.

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