scholarly journals Series-Based Solution for Analysis of Simply Supported Rectangular Thin Plate with Internal Rigid Supports

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Abubakr E. S. Musa ◽  
Husain J. Al-Gahtani
Keyword(s):  
Analytical Solution ◽  
Bending Moment ◽  
Accurate Solution ◽  
Rectangular Plates ◽  
Compatibility Conditions ◽  
Element Analysis ◽  
Simply Supported ◽  
The Finite Element Analysis ◽  
Rigid Supports ◽  
The Given

In this study, Navier’s solution for the analysis of simply supported rectangular plates is extended to consider rigid internal supports. The proposed method offers a more accurate solution for the bending moment at the critical section and therefore serves as a better analytical solution for design purposes. To model the plate-support interaction, the patched areas representing the contact between the plate and supports are divided into groups of cells. The unknown internal reactions at the centers of the divided cells are obtained by satisfying the compatibility conditions at the centers of the cells. Three numerical examples are presented to demonstrate the accuracy of the proposed analytical solution. The given examples reveal good agreements with those obtained by the finite element analysis. In addition, they show the advantage of the new solution as compared to the existing analytical solution which inaccurately estimates the location and magnitude of the maximum bending moment.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

scholarly journals A Review on Numerical Analysis of RC Flat Slabs Exposed to Fire

2020 ◽  
Vol 27 (1) ◽  
pp. 1-5
Author(s):  
Hanadi Naji ◽  
Nibras Khalid ◽  
Mutaz Medhlom
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Analysis ◽  
Bending Moment ◽  
Mechanical And Thermal Properties ◽  
Vertical Deflection ◽  
Element Analysis ◽  
Flat Slabs ◽  
Numerical Studies ◽  
The Finite Element Analysis

This paper aims at presenting and discussing the numerical studies performed to estimate the mechanical and thermal behavior of RC flat slabs at elevated temperature and fire. The numerical analysis is carried out using finite element programs by developing models to simulate the performance of the buildings subjected to fire. The mechanical and thermal properties of the materials obtained from the experimental work are involved in the modeling that the outcomes will be more realistic. Many parameters related to fire resistance of the flat slabs have been studied and the finite element analysis results reveal that the width and thickness of the slab, the temperature gradient, the fire direction, the exposure duration and the thermal restraint are important factors that influence the vertical deflection, bending moment and force membrane of the flat slabs exposed to fire. However, the validation of the models is verified by comparing their results to the available experimental date. The finite element modeling contributes in saving cost and time consumed by experiments.

Guidelines for the Use of Approximations in Shock Response Analysis of Electronic Assemblies

1993 ◽  
Vol 115 (1) ◽  
pp. 124-130 ◽  
Author(s):  
R. F. Keltie ◽  
K. J. Falter
Keyword(s):  
Finite Element Analysis ◽  
Rigid Body ◽  
Simple Structure ◽  
Response Analysis ◽  
Element Analysis ◽  
Simply Supported ◽  
Inappropriate Use ◽  
The Finite Element Analysis ◽  
Shock Response ◽  
Electronic Assemblies

In order to reduce the time and effort to create models and prevent excessive computer run times, approximations and simplifications are often used in the finite element analysis of the shock response of electronic assemblies. Typical approximations which might be used include neglecting components which have small masses and considering highly stiff connections as rigid connections. It is difficult to determine under what conditions approximations may be applied and to what extent they affect a model’s accuracy. Rather than depending only on an analyst’s experience or intuition, guidelines are desirable to prevent the inappropriate use of approximations. To illustrate the methodology for developing guidelines, this paper examines approximations involving a simple structure which is representative of structures found in electronic assemblies. This structure consists of a rigid body attached by a flexible connection to a beam. Approximations considered were: approximating the stiffness of the connection, neglecting the mass of the rigid body, and approximating the boundary conditions of the beam as either simply-supported or clamped. In developing guidelines a large number of individual analyses were necessary. An important aspect of this investigation is our proposal for a concise format for presenting the results of many analyses. The techniques which were used to reduce the amount of data to be presented are discussed.

Free Vibration Analysis of a Simply Supported Rectangular Tank Partially Filled With a Liquid

2010 ◽  
Author(s):  
Kyeong-Hoon Jeong ◽  
Jin-Seok Park ◽  
Won-Jae Lee
Keyword(s):  
Boundary Conditions ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Ideal Liquid ◽  
Rectangular Plates ◽  
Element Analysis ◽  
Displacement Potential ◽  
Simply Supported ◽  
Rectangular Tank ◽  
Liquid Displacement

This paper presents a theoretical analysis for the hydroelastic vibration of a rectangular tank partially filled with an ideal liquid. The wet dynamic displacement of the tank is approximated by combining the orthogonal polynomials satisfying the simply supported boundary conditions, since the rectangular tank is composed of four rectangular plates. As the facing rectangular plates are geometrically identical, the vibration modes of the facing plates can be divided into two categories: symmetric modes and asymmetric modes with respect to the vertical centerlines of the plates. The liquid displacement potential satisfying the boundary conditions is derived and the wet dynamic modal functions of the four plates are expanded by the finite Fourier transformation for a compatibility requirement along the contacting surface between the tank and the liquid. The natural frequencies of the rectangular tank in the wet condition are calculated by using the Rayleigh-Ritz method. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results.

Plastic Collapse Assessment Procedure for Vessel With Local Thin Area Simultaneously Subjected to Internal Pressure and External Bending Moment

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Shinji Konosu ◽  
Norihiko Mukaimachi
Keyword(s):  
Internal Pressure ◽  
Pressure Ratio ◽  
Bending Moment ◽  
Outer Diameter ◽  
Assessment Procedure ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Tension And Compression ◽  
And Storage ◽  
Moment Ratio Diagram

Assessment of the local thin area should be undertaken for both tension and compression bending. In this paper, simplified reference stresses for a flaw in a cylinder are proposed. By using these results, a newly developed p-M (internal pressure ratio and external bending moment ratio) diagram which can evaluate the collapse condition for pressure equipment such as vessels, piping, and storage tanks with a local thin area simultaneously subjected to internal pressure p and external bending moment M due to earthquake, etc., is proposed. The p-M line is verified by comparison with the finite element analysis results and the numerous results of experiment for a cylinder with a volumetric flaw obtained through the reference literatures. It was clarified that the differences in collapse limit between the p-M line and DNV guideline under both internal pressure and compression moment became evident where the outer diameter/wall thickness of a cylinder is large and the yield ratio of the material is small.

scholarly journals Calculation of fracture mechanic parameters via FEM for some cracked plates under different loads

2006 ◽  
Vol 28 (2) ◽  
pp. 83-93 ◽  
Author(s):  
Ngo Huong Nhu ◽  
Nguyen Truong Giang
Keyword(s):  
Inclined Crack ◽  
Gravity Dams ◽  
Element Analysis ◽  
Cracked Plates ◽  
Failure State ◽  
The Finite Element Analysis ◽  
Arbitrary Position ◽  
Characteristic Values ◽  
The Given ◽  
Good Agreement

This paper describes some results in analyzing cracked plates via FEM based on the procedures in CASTEM 2000 [1]. The basic methods for computing the crack parameters by the finite element analysis are presented. Some programs written by GIBIAN languages to solve problems for cracked plates are given. In possible cases, the numerical results are composed with analytical solution or testing result that gives a good agreement. The influence of plate configurations, the crack length, the external load type on the crack characteristic values are considered. The numerical analysis for inclined crack at angle and in arbitrary position of plate, the crack at hole in the plate, the crack of gravity dams are realized. The given results and programs can be applied to practical problems for controlling the brittle failure state of a structure.

Forced Vibrations of Thin, Elastic, Rectangular Plates with Edges Elastically Restrained Against Rotation

1977 ◽  
Vol 21 (01) ◽  
pp. 24-29
Author(s):  
E. A. Susemihl ◽  
P. A. A. Laura
Keyword(s):  
Bending Moment ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Edge Conditions ◽  
Approach Infinity ◽  
Square Plate ◽  
Elastic Rectangular Plate ◽  
Elastically Restrained ◽  
The Galerkin Method

Polynomial coordinate functions and the Galerkin method are used to determine the response of a thin, elastic, rectangular plate with edges elastically restrained against rotation and subjected to sinusoidal excitation. It is shown that when the flexibility coefficients approach infinity (simply supported edge conditions) the calculated results practically coincide with the exact solution in the case of a square plate when four terms of the expansion are used. Dynamic displacement and bending moment amplitudes are tabulated for different length-to-width ratios, flexibility coefficients, and frequency values.

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