Finite strip analysis of continuous structures

1988 ◽  
Vol 15 (3) ◽  
pp. 424-429 ◽  
Author(s):  
M. S. Cheung ◽  
Wenchang Li
Keyword(s):  
Finite Element ◽  
Transverse Direction ◽  
Shape Function ◽  
Longitudinal Direction ◽  
Plate Bending ◽  
Continuous Beam ◽  
Numerical Examples ◽  
Finite Strip ◽  
Element Shape ◽  
Plate Type

The eigenfunctions of a continuous beam are found numerically. The folded plate type of finite strip with intermediate supports is formulated by combining such an eigenfunction in the longitudinal direction with an appropriate finite element shape function in the transverse direction. The numerical examples given in this paper, such as the continuous beam and plate, demonstrate the advantages of this method: simplicity, accuracy, and convenience. Key words: finite strip, continuous structure, eigenfunction, folded plate, plate bending.

scholarly journals A Study on Seismic Isolation of Shield Tunnel Using Quasi-Static Finite Element Method

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Can Li ◽  
Weizhong Chen ◽  
Wusheng Zhao ◽  
Takeyasu Suzuki ◽  
Yoshihiro Shishikura
Keyword(s):  
Finite Element ◽  
Shear Modulus ◽  
Seismic Isolation ◽  
Transverse Direction ◽  
Longitudinal Direction ◽  
Isolation Effect ◽  
Poisson's Ratio ◽  
Shield Tunnel ◽  
Isolation System ◽  
Isolation Layer

Using a quasi-static method based on an axisymmetric finite element model for seismic response analysis of seismically isolated tunnels, the seismic isolation effect of the isolation layer is studied, and the seismic isolation mechanism of the isolation layer is clarified. The results show that, along the longitudinal direction of the tunnel, the seismic isolation effect is mainly affected by the shear modulus of the isolation material. The smaller the shear modulus is, the more evident the seismic isolation effect is. This is due to the tunnel being isolated from deformation of its peripheral ground through shear deformation of the isolation layer. However, along the transverse direction of the tunnel, the seismic isolation effect is mainly affected by the shear modulus and Poisson’s ratio of the isolation material. When Poisson’s ratio is close to 0.5, a seismic isolation effect is not evident because the tunnel cannot be isolated from deformation of its peripheral ground through compression deformation of the isolation layer. Finally, a seismic isolation system comprising a shield tunnel in which flexible segments are arranged at both ends of an isolation layer is proposed, and it is proved that the seismic isolation system has significant seismic isolation effects both on the longitudinal direction and on the transverse direction.

scholarly journals ELEMENT DKT_CST FOR ANALYSIS OF LAMINATED ANISOTROPIC PLATES/ELEMENTAS DKT_CST SLUOKSNIUOTŲ ANIZOTROPINIŲ PLOKŠTELIŲ ANALIZEI

2000 ◽  
Vol 6 (5) ◽  
pp. 351-356
Author(s):  
Edvard Michnevič ◽  
Rimantas Belevičius
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Triangular Element ◽  
Plate Bending ◽  
Anisotropic Plates ◽  
Numerical Examples ◽  
Out Of Plane ◽  
Bending Problems ◽  
Slab Bending ◽  
Plate Bending Problem

The new finite element of multilayered built up with an arbitrary series of layers plate for plate bending problem is formulated on the ground of widely used, effective finite element Discrete Kirchhof Theory (DKT). The material of each layer is supposed to be different and orthotopic. Triangular element has 6 d.o.f.'s at each of 3 nodal points: 3 displacements and 2 rotations about co-ordinate axes. The 6th fictitious rotation about axis perpendicular to the element is also introduced due to numerical requirements. The element takes into account all the in-plane/out-of-plane effects except the shear. The element could find an application in the slab bending problems or in the plate, where the shear influence could be neglected, bending problems. The numerical examples are presented. Present solutions are compared with available analytical and numerical solutions.

scholarly journals THE LAYERED ELEMENT DKT_CST FOR ANALYSIS OF ANISOTROPIC PLATES

2007 ◽  
Vol 13 (1) ◽  
pp. 41-46
Author(s):  
Edvard Michnevič
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Triangular Element ◽  
Plate Bending ◽  
Anisotropic Plates ◽  
Numerical Examples ◽  
Out Of Plane ◽  
Bending Problems ◽  
Slab Bending ◽  
Plate Bending Problem

The new finite element of multilayered built up with an arbitrary series of layers plate for plate bending problem is formulated on the ground of widely used, effective finite element Discrete Kirchhof Theory (DKT). The material of each layer is supposed to be different and orthotropic. Triangular element has 6 d.o.f.’s at each of 3 nodal points: 3 displacements and 3 rotations about co‐ordinate axes. The element takes into account all the in‐plane/out‐of‐plane effects except for shear. The element could find an application in the slab bending problems or in the plate, where the shear influence could be neglected, bending problems. Numerical examples are presented. Present solutions are compared with available analytical and numerical solutions.

A New Strain Based Sector Finite Element for Plate Bending Problems

2017 ◽  
Vol 31 ◽  
pp. 1-13 ◽  
Author(s):  
Sifeddine Abderrahmani ◽  
Toufik Maalem ◽  
Abdallah Zatar ◽  
Djamal Hamadi
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Finite Elements ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Plate Bending ◽  
Numerical Examples ◽  
Bending Problems ◽  
Thin Plate Bending ◽  
Three Degrees Of Freedom

The purpose of this paper is to present the formulation of a new sector finite element based on the strain approach for the numerical analysis of circular thin plate bending. The element is named SBSPK and has four nodes and three degrees of freedom per node (3 d.o.f./node). From several numerical examples, it is shown that convergence can be achieved with the use of only a small number of finite elements. The results obtained are compared with analytical and available numerical solutions.

Large Amplitude Free Flexural Vibration of Stiffened Plates Using Superparametric Element

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Saleema Panda ◽  
Manoranjan Barik
Keyword(s):  
Displacement Field ◽  
Large Amplitude ◽  
Shape Function ◽  
Flexural Vibration ◽  
Stiffened Plates ◽  
Plate Bending ◽  
Arbitrary Geometry ◽  
Numerical Examples

The present paper studies the nonlinear free flexural vibration of stiffened plates. The analysis is performed using a superparametric element. This element consists of an ACM plate-bending element along with in-plane displacements to represent the displacement field, and cubic serendipity shape function is used to define the geometry. The element can accommodate any arbitrary geometry, and the stiffeners either straight or curvilinear are modeled such that these can be placed anywhere on the plate. A number of numerical examples are presented to show its efficacy.

Finite Element Incremental Approach and Exact Rigid Body Inertia

1995 ◽  
Author(s):  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Shape Function ◽  
Rigid Bodies ◽  
Shape Functions ◽  
Mass Moment ◽  
Nodal Coordinates ◽  
Inertia Properties ◽  
Element Shape ◽  
Body Inertia

Abstract In the dynamics of multibody systems that consist of interconnected rigid and deformable bodies, it is desirable to have a formulation that preserves the exactness of the rigid body inertia. As demonstrated in this paper, the incremental finite element approach, which is often used to solve large rotation problems, does not lead to the exact inertia of simple structures when they rotate as rigid bodies because the physical nodal coordinates can not be used to describe large rotations in the case of beams and plates. Nonetheless, the exact inertia properties, such as the mass moments of inertia and the moments of mass, of the rigid bodies can be obtained using the finite element shape functions that describe large rigid body translations by introducing an intermediate element coordinate system. The results of application of the parallel axis theorem can be obtained using the finite element shape functions by simply changing the element nodal coordinates. A simple rigid body rotation, however, can cause a significant error if the element shape function and the nodal coordinates are used to evaluate the inertia properties of bodies that undergo large rigid body rotations. As demonstrated in this investigation, the exact rigid body inertia properties in case of rigid body rotations can be obtained using the shape function if the nodal coordinates are defined using trigonometric functions that lack a physical meaning. Linearization of the nodal coordinate vector can lead to different results when different methods are used to define the rigid body inertia. For example, the calculation of the mass moment of inertia using position coordinates only leads to results which are different from those obtained using energy expressions or the laws of motion.

A GFEM With Local Gradient Smoothed Approximation for 2D Solid Mechanics Problems

2020 ◽  
Author(s):  
Jinsong Tang ◽  
Linfang Qian ◽  
Guangsong Chen
Keyword(s):  
Finite Element ◽  
Basis Function ◽  
Taylor Expansion ◽  
Solid Mechanics ◽  
Shape Function ◽  
Displacement Function ◽  
Field Function ◽  
Integration Schemes ◽  
Local Gradient ◽  
Element Shape

Abstract In this paper, a generalized finite element method (GFEM) with local gradient smoothed approximation (LGS-GFEM) using triangular meshes is proposed. The displacement field function of LGS-GFEM consists of the finite element shape function and the node displacement function. In order to obtain the nodal displacement function, the second order Taylor expansion is considered. The derivative term in Taylor expansion is obtained by using gradient smoothed technique in a smoothed domain. The displacement in smoothed operation is interpolated by polynomial basis function and radial basis function. Two kinds of integration schemes are considered, i.e. LGS-GFEM-I and LGS-GFEM-II respectively. The smoothed composite shape function of LGS-GFEM retains the ideal Kronecker property of the finite element shape function. Besides, the proposed LGS-GFEM has some other important properties such as no extra DOFs, linear independent, etc. The superiority of LGS-GFEM including high accuracy, rapid error convergence and temporal stability, is demonstrated by two representative numerical examples of static and free vibration, and compared with the classical finite element of triangular (FEM-T3) and quadrilateral (FEM-Q4) elements.

AISI 1141

Alloy Digest ◽  
1983 ◽  
Vol 32 (3) ◽  
Keyword(s):  
Carbon Steel ◽  
Transverse Direction ◽  
Longitudinal Direction ◽  
Heat Treating ◽  
Automatic Machine ◽  
Steel Mills ◽  
Light Duty ◽  
High Production ◽  
Ball Joints ◽  
Machining Characteristics

Abstract AISI 1141 is a resulfurized carbon steel containing nominally 1.50% manganese and 0.08-0.13% sulfur to give it free-machining characteristics. It has relatively low hardenability. Its ductility and toughness are fairly good in the longitudinal direction but tend to be low in the transverse direction. It is highly recommended for high-production automatic-machine products. Among its many uses are screws, bolts, ball joints, spindles and light-duty gears. This datasheet provides information on composition, physical properties, hardness, and tensile properties. It also includes information on forming, heat treating, machining, joining, and surface treatment. Filing Code: CS-93. Producer or source: Carbon steel mills.

Quality Assessment of Weldable Steel Mark P355NH from Decompression Chamber Construction for Diving

2012 ◽  
Vol 217-219 ◽  
pp. 2381-2387
Author(s):  
Doru Romulus Pascu ◽  
Radu Alexandru Roşu ◽  
Iuliana Duma ◽  
Horia Daşcău
Keyword(s):  
Test Temperature ◽  
Transverse Direction ◽  
Mechanical Characteristics ◽  
Longitudinal Direction ◽  
Pressure Vessels ◽  
Fine Grained ◽  
Weldable Steel ◽  
Breaking Energy ◽  
Fine Grained Steels ◽  
Selection Of

Non-alloyed P355NH steel according to EN 10028-3:2003 belongs to a group of fine-grained steels for pressure vessels being used in welded construction at decompression chamber for divers. Values of the chemical, structural and mechanical characteristics and steel toughness experimentally determined fit the analyzed steel in P355NH steel group according to EN 10028-3:2003. The toughness of the analyzed steel at the test temperature of -30°C is characterized by high values of fracture energy KV in longitudinal direction between 48 and 86 J and on transverse direction between 17 and 34J. Steel toughness at the test temperature of -30°C required by ABS standard (in Section 4/5.3 and Table 1) provides for breaking energy KV of min. 35J, with ductile fracture surfaces, value that is not respected at some lots of the three batches (A, B, C) of steel. Finally, based on the direct correlation established between HV10 hardness of the fine structure and the toughness it was made a selection of the lots of non-alloy steel P355NH which correspond to ABS norm for welded construction of the decompression chamber for divers

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