scholarly journals Engineering methods for calculation of elements from combined glued timber

2020 ◽  
Vol 11 (2) ◽  
pp. 79-90
Author(s):  
S. I. Bilyk ◽  
D. V. Mykhaіlovskyi
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Software Package ◽  
Strength Class ◽  
Rectangular Cross Section ◽  
Analytical Calculation ◽  
The Finite Element Method ◽  
Cross Sectional ◽  
Numerical Studies ◽  
Reduced Modulus

Extensive world experience in the implementation of building structures made of timber, in particular glued timber, for various purposes confirms the feasibility of their use. This is facilitated by the fact that glued timber effectively accumulates the positive properties of timber as a structural material level the shortcomings of solid timber. One of the types of constructions of glued timber are constructions of combined glued timber. Taking into account the structure and features of elements of combined glued timber of rectangular cross section, for a detailed analysis of the stress-strain state, a method is proposed, which consists in applying to standard formulas for calculating the reduced cross-sectional characteristics: reduced area, reduced moment of inertia, reduced moment of resistance. To calculation, the elements of combined glued timber of rectangular cross section according to the second limit state (serviceability), it is proposed to use the reduced modulus of elasticity of the section to the boards of the outer layers. To analyze the proposed method, a number of numerical studies of beams of combined and glued timber of the same strength class using analytical calculation methods and using the finite element method in the software package LIRA-CAD, using three-dimensional and flat finite elements. Numerical studies show that the results of calculations of beams of combined glued and glued timber of the same strength class differ within 20% in the direction of increasing the values of deflections and normal stresses in the elements of combined glued timber. Finite element calculations in the software package LIRA-CAD beams of combined and glued timber of the same strength class modeled volumetric and flat showed almost complete coincidence of results with a discrepancy of up to 2%, which suggests the need to significantly simplify the modeling, set elements from glued timber with flat finite elements. It is confirmed that the analytical calculation of beams of combined glued timber is recommended to be carried out according to the proposed method. The proposed technique allows to take into account the thickness and mechanical characteristics for the strength class of each board of which the glued cross section of the element, which significantly expands the range of use of combined glued timber. The high level of coincidence (within 5%) of the proposed analytical method with determination of the given cross-sectional characteristics with the results obtained by the finite element method for different cross-sections and spans of beams is confirmed, which allows to assert the expediency of its application in engineering calculations. In addition, the modeling of structures made of combined glued timber is possible with rod elements with the provision of the reduced modulus of elasticity according to the proposed method, which greatly simplifies the calculation of complex rod systems.

Saint-Venant Decay Rates for the Rectangular Cross Section Rod

2004 ◽  
Vol 71 (3) ◽  
pp. 429-433 ◽  
Author(s):  
N. G. Stephen ◽  
P. J. Wang
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Transfer Matrix ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Decay Rates ◽  
Elastic Rod ◽  
Cross Sectional ◽  
Element Transfer

A finite element-transfer matrix procedure developed for determination of Saint-Venant decay rates of self-equilibrated loading at one end of a semi-infinite prismatic elastic rod of general cross section, which are the eigenvalues of a single repeating cell transfer matrix, is applied to the case of a rectangular cross section. First, a characteristic length of the rod is modelled within a finite element code; a superelement stiffness matrix relating force and displacement components at the master nodes at the ends of the length is then constructed, and its manipulation provides the transfer matrix, from which the eigenvalues and eigenvectors are determined. Over the range from plane stress to plane strain, which are the extremes of aspect ratio, there are always eigenmodes which decay slower than the generalized Papkovitch-Fadle modes, the latter being largely insensitive to aspect ratio. For compact cross sections, close to square, the slowest decay is for a mode having a distribution of axial displacement reminiscent of that associated with warping during torsion; for less compact cross sections, slowest decay is for a mode characterized by cross-sectional bending, caused by self-equilibrated twisting moment.

Why Is (111) Silicon a Better Mechanical Material for MEMS: Torsion Case

2003 ◽  
Author(s):  
Donghun Kwak ◽  
Jongpal Kim ◽  
Sangjun Park ◽  
Hyoungho Ko ◽  
Dong-Il Cho
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Silicon Wafers ◽  
Torsional Stiffness ◽  
Rotational Inertia ◽  
The Finite Element Method ◽  
Element Type ◽  
Simulation Results

This paper shows that using the Finite Element Method (FEM), the torsional stiffness of silicon varies by the least amount on silicon (111) with respect to crystallographic directions, when compared to silicon (100) and (110). The used simulator is ANSYS 5.7 with the element type of Solid 64. As a simulation model, we use a simple torsion system, in which a rotational inertia is attached to the center of clamped-clamped beam with a rectangular cross-section. From the results of the modal analysis, the torsional stiffness is derived using the formula between the natural frequency and the torsional stiffness. Simulation results show that the maximum variations of the torsional stiffness on silicon (111), (100) and (110) are 2.3%, 26.5%, and 31.2%, respectively. This implies that on <100> and <110> silicon wafers, substantially different physical dimensions are necessary for devices with the same torsional characteristics, but with different orientations. Therefore, <111> silicon wafers represent a more suitable substrate to design and fabricate torsional micro and nano systems.

scholarly journals Shape Optimization of Bone-Bonding Subperiosteal Devices with Finite Element Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Takeshi Ogasawara ◽  
Masayoshi Uezono ◽  
Kazuo Takakuda ◽  
Masanori Kikuchi ◽  
Shoichi Suzuki ◽  
...  
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Bonding Strength ◽  
Clinical Performance ◽  
Rectangular Cross Section ◽  
Optimum Shape ◽  
Bone Surface ◽  
Element Analysis ◽  
Cross Sectional ◽  
Rapid Acquisition

Subperiosteal bone-bonding devices have been proposed for less invasive treatments in orthodontics. The device is osseointegrated onto a bone surface without fixation screws and is expected to rapidly attain a bone-bonding strength that successfully meets clinical performance. Hence, the device’s optimum shape for rapid and strong bone bonding was examined in this study by finite element analyses. First, a stress analysis was performed for a circular rod device with an orthodontic force parallel to the bone surface, and the estimate of the bone-bonding strength based on the bone fracture criterion was verified with the results of an animal experiment. In total, four cross-sectional rod geometries were investigated: circular (Cr), elliptical (El), semicircular (Sc), and rectangular (Rc). By changing the height of the newly formed bone to mimic the progression of new bone formation, the estimation of the bone-bonding strength was repeated for each geometry. The rod with the Rc cross section exhibited the best performance, followed by those with the Sc, El, and Cr cross sections, from the aspects of the rapid acquisition of strength and the strength itself. Thus, the rectangular cross section is the best for rod-like subperiosteal devices for rapid bone bonding.

Free Warping Analysis and Numerical Implementation

2016 ◽  
Vol 825 ◽  
pp. 141-148 ◽  
Author(s):  
Karel Mikeš ◽  
Milan Jirásek
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Laplace Equation ◽  
Solution Algorithm ◽  
Point Of View ◽  
Warping Function ◽  
Numerical Implementation ◽  
Finite Element Code ◽  
The Finite Element Method ◽  
Cross Sectional

This article deals with the mathematical description and numerical implementation of the free warping problem. The solution of the warping problem is given by a warping function obtained by solving the Laplace equation with a corresponding boundary condition. An analytical solution is available only for a limited number of specific cross-sectional shapes such as ellipse or rectangle. For the solution of a general cross section, the Laplace equation must be solved numerically by the finite element method. From a mathematical point of view, the free warping problem can be described in the same way as the heat transfer phenomena, but in the numerical implementation, there are several features specific to warping analysis.The solution algorithm has been implemented in the OOFEM open-source finite element code [1] and verification has been done on several examples with known analytical solutions.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

scholarly journals Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

2018 ◽  
Vol 5 (2) ◽  
pp. 171717 ◽  
Author(s):  
Srivatsa Bhat K ◽  
Ranjan Ganguli
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Beam Equation ◽  
The Finite Element Method ◽  
Rayleigh Beam ◽  
Uniform Beam ◽  
Governing Differential Equation ◽  
The Given

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

Numerical Investigation on Diffusion Slot Hole With Various Cross-Sectional End Shapes

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Bai-Tao An ◽  
Jian-Jun Liu
Keyword(s):  
Cross Section ◽  
Film Cooling ◽  
Separation Bubble ◽  
Rectangular Cross Section ◽  
Pressure Ratio ◽  
Smooth Transition ◽  
Shape Variation ◽  
Cross Sectional ◽  
Cooling Effectiveness ◽  
Shaped Hole

The diffusion hole constructed on a slot-type cross section has the potential to obtain high film cooling performance. However, the end shape of the cross section can greatly affect film cooling characteristics. This study examined eight cases of diffusion slot holes with various cross-sectional end shapes. The comparison of the eight diffusion slot holes and a typical fan-shaped hole was performed with a flat plate model using a three-dimensional (3D) steady computational fluid dynamics (CFD) method. The rectangular cross section had an aspect ratio of about 3.4. The end shape variation can be described based on sidewall contraction location, size, and form. The simulations were performed under an engine-representative condition of mainstream inlet Mach number 0.3 and turbulence intensity 5.2%. The simulated results showed that a strip separation bubble caused by inlet “jetting effect” occurs near the downstream wall of the diffusion slot hole and interacts with the diffusion flow. The different end shape of the rectangular cross section leads to different sidewall static pressure and exit velocity profiles, thereby produces three cooling effectiveness patterns, single-peak, bipeak, and tripeak patterns. The tripeak pattern produces higher cooling effectiveness and relatively uniform film coverage. The structure with moderate contraction and smooth transition on two sides of the downstream wall favors creation of a tripeak pattern. Compared with the fan-shaped hole, the discharge coefficient of diffusion slot hole is slightly small in low pressure ratio range, the pressure loss ratio has little difference.

Improving the honing accuracy of the holes of stepped thin-walled cylinders

2021 ◽  
pp. 49-54
Author(s):  
V.A. Ogorodov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cutting Forces ◽  
Software Package ◽  
The Finite Element Method ◽  
Radial Forces ◽  
Thin Walled ◽  
Hole Machining ◽  
Deform 3D ◽  
Walled Cylinder

Different ways of fixing of stepped thin-walled cylinders during honing are analyzed. The conditions for increasing the accuracy of hole machining are determined on the basis of unevenness of cylinder deformations from clamping forces and radial forces simulating cutting forces. The studies used the finite element method and the DEFORM-3D V6.1 software package. Keywords: honing, stepped thin-walled cylinder, hole, accuracy, fixing method, deformation, unevenness, DEFORM-3D V6.1 software package. [email protected]

Fatigue damage in bending of reinforced concrete frames using non-destructive tests for dynamic strength of the cylinder

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Dragan D. Milašinović ◽  
Aleksandar Landović ◽  
Danica Goleš
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fatigue Damage ◽  
Cross Section ◽  
Modal Parameters ◽  
The Finite Element Method ◽  
Concrete Frames ◽  
Content Type ◽  
Non Destructive

PurposeThe purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending.Design/methodology/approachThe problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems.FindingsThe modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response.Originality/valueThe paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

scholarly journals The creation of a computational model of corrugated beams using the author’s program “GOPRO”

2018 ◽  
Vol 251 ◽  
pp. 04007 ◽  
Author(s):  
Vadim Alpatov ◽  
Alexey Lukin ◽  
Irina Laguta
Keyword(s):  
Finite Element ◽  
Computational Model ◽  
Cross Section ◽  
Geometrical Shape ◽  
File Format ◽  
Element Mesh ◽  
Automated Generation ◽  
Numerical Studies ◽  
Geometrical Scheme ◽  
The Web

The program «Gofro» is intended for the automated generation of data on the geometrical scheme of the beam with corrugated or plane web for further use in design complexes. The program has got a window interface, and it consists of one module for the input of feed da-ta, for calculation and for the display of its results in txt file format. The program offers a possibility to choose the outline of the structure, the profile of the web, the type of cross-section, and to set other parameters of the structure. When building up the model with the help of the author program «Gofro» and GMSH preprocessor for the automatic genera-tion of finite element mesh, the correctness of geometrical shape of elements is monitored by the algorithms that are input in the preprocessor. The author compares the time re-quired to create the models using the author program and GMSH preprocessor and using the standard resources of «Lira» software system. The authors performed numerical studies of various I-beams created in the program «GOPRO».

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