scholarly journals Unified Fundamental Formulas for Static Analysis of Pin-Jointed Bar Assemblies

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 994
Author(s):  
Pei Zhang ◽  
Huiting Xiong ◽  
Junsheng Chen
Keyword(s):  
External Disturbance ◽  
Full Rank ◽  
Equilibrium Equations ◽  
Force Method ◽  
Axial Forces ◽  
The Matrix ◽  
Structural Responses ◽  
Internal Forces ◽  
Stress States ◽  
External Loads

The initial axial forces of members—whatever caused by prestress or external loads—may strongly change the mechanical properties of pin-jointed bar assemblies, to enhance, or even establish their structural stiffness. The structural responses under external disturbance cannot be calculated accurately if the influence of initial axial forces has not been considered appropriately. In this paper, an analytic theory considering the effect of initial internal forces is developed on the basis of linear elasticity hypothesis. The fundamental formulas proposed finally include generalized equilibrium equations and generalized compatibility equations, both of which have square coefficient matrices of full rank being transposed with each other. Generally, this method can be regarded as an extended version of a traditional force method considering the stiffening effect of initial internal forces. Compared with the matrix force method, it has a wider application scenario since few redundant simplifications are employed in the derivation of the formulas. In comparison with the displacement-based algorithm, the proposed method has the inherent advantages of the force method—the physical concepts of each item in equations are fairly explicit; and the combination coefficients of self-stress states and mechanisms are determined simultaneously in solving the structural responses. Thus, it is very helpful for us to essentially comprehend the principle that the pin-jointed bar assemblies resist the external loads.

Research of stamping of unequal channel bars. Part 3. Force parameters and shape change of the billet when extruding channels. 1. Kinematic and stress states of the billet

2021 ◽  
pp. 65-71
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Flow ◽  
Complete System ◽  
Shape Change ◽  
Plane Deformation ◽  
System Of Equations ◽  
Flow Rates ◽  
Die Forging ◽  
The Matrix ◽  
Stress States ◽  
Theory Of Plastic Flow

On the basis of the complete system of equations of the theory of plastic flow, the kinematic and stress states of the billet are determined when the channels are extruded under conditions of plane deformation of the misaligned position of the punch and the matrix. Keywords: die forging, extrusion, misaligned position, punch, matrix, plane deformation, plastic flow rates, stresses. [email protected]

Study of the Influence of the Beam-Column Line Stiffness Ratio on the Frame Structure Load Capacity Based on MATLAB

2011 ◽  
Vol 71-78 ◽  
pp. 4194-4198
Author(s):  
Shao Qin Zhang ◽  
Hua Hu Cheng
Keyword(s):  
Engineering Design ◽  
Carrying Capacity ◽  
Calculated Result ◽  
Load Capacity ◽  
Frame Structure ◽  
Stiffness Ratio ◽  
Displacement Method ◽  
Structure Form ◽  
The Matrix ◽  
Internal Forces

Statically indeterminate frame, composed of beams and columns, is a widely used structure form in civil engineering. The frame carrying capacity under various actions is related to the absolute stiffness of frame components and relative beam-column line stiffness ratio. The matrix displacement method and programming based on MATLAB were employed in this study to calculate the internal forces and displacements of a 2-bay 2-story frame structure under the action of horizontal loads. The influence of the beam-column line stiffness ratio on the frame load capacity was discussed based on the calculated result. Furthermore some advises were provided about the reasonable beam-column line stiffness ratio for engineering design.

scholarly journals The Use of the Collocation Algorithm for Estimating the Deformations of Soil-Shell Objects Made of Corrugated Sheets

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Czesław Machelski
Keyword(s):  
Strain Gauges ◽  
Boundary Constraints ◽  
Axial Forces ◽  
Collocation Points ◽  
Geodetic Measurements ◽  
Significant Divergence ◽  
Internal Forces ◽  
Support Conditions ◽  
Static Conditions ◽  
The Impact

AbstractThe algorithm presented in this paper is intended for the analysis of deformations of shells in the construction phase of soil-shell objects when strain gauges and geodetic measurements are used. During the construction of such an object, large displacement values occur and the impact of axial forces on the displacement of a corrugated metal sheet is small. Internal forces (strain gauges), as well as the displacements of a selected circumferential band of the shell are determined directly from such observations.The paper presents two examples of the analysis of large span shell structures of constructed objects, as well as the assessment of the effectiveness of the finite difference method (FDM) in beam schemes. Good deformation mapping was indicated using the collocation algorithm and the differential approach to the solution when there is a dense mesh and regular distribution of measuring points. In the analysed examples, a significant divergence between the support conditions adopted in the FEM calculation models and the actual static conditions in the objects was indicated. The collocation algorithm is especially designed for such situations. Collocation points in such a solution are used to consider a beam – separated from a structure and without boundary constraints, but with specific changes in curvature – as a reference system, which is determined from the geodetic measurements of two collocation points.

scholarly journals Calculation of the goffered multilayered composite cylindrical shells by using the finite element method

1999 ◽  
Vol 21 (2) ◽  
pp. 116-128
Author(s):  
Pham Thi Toan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
The Finite Element Method ◽  
Multilayered Composite ◽  
Internal Forces ◽  
External Loads ◽  
Element Method ◽  
Composite Cylindrical Shells

In the present paper, the goffered multilayered composite cylindrical shells is directly calculated by finite element method. Numerical results on displacements, internal forces and moments are obtained for various kinds of external loads and different boundary conditions.

scholarly journals Calculation of thin isotropic shells beyond the elastic limit by the method of elastic solutions

2018 ◽  
Vol 196 ◽  
pp. 01014 ◽  
Author(s):  
Avgustina Astakhova
Keyword(s):  
Elastic Limit ◽  
Physical Nonlinearity ◽  
Elasticity Tensor ◽  
Thin Shells ◽  
Equilibrium Equations ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Internal Forces

The paper focuses on the model of calculation of thin isotropic shells beyond the elastic limit. The determination of the stress-strain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method. In the present work the building of the solution based on the equilibrium equations and geometric relations of linear theory of thin shells in curved coordinate system α and β, and the relations between deformations and forces based on the Hirchhoff-Lave hypothesis and the small elastic-plastic deformations theory are presented. Internal forces tensor is presented in the form of its expansion to the elasticity tensor and the additional terms tensor expressed the physical nonlinearity of the problem. The functions expressed the physical nonlinearity of the material are determined. The relations that allow to determine the range of elastic-plastic deformations on the surface of the present shell and their changing in shell thickness are presented. The examples of the calculation demonstrate the convergence of elastic-plastic deformations method and the range of elastic-plastic deformations in thickness in the spherical shell. Spherical shells with the angle of half-life regarding 90 degree vertical symmetry axis under the action of equally distributed ring loads are observed.

An Analytical Solution for Transversely Isotropic Simply Supported Thick Rectangular Plates Using Displacement Potential Functions

2011 ◽  
Vol 46 (2) ◽  
pp. 121-142 ◽  
Author(s):  
M Nematzadeh ◽  
M Eskandari-Ghadi ◽  
B Navayi Neya
Keyword(s):  
Isotropic Material ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Potential Functions ◽  
Constant Thickness ◽  
Rectangular Plates ◽  
Displacement Potential ◽  
Simply Supported ◽  
Axial Forces ◽  
Internal Forces

Using a complete set of displacement potential functions, the exact solution of three-dimensional elasticity equations of a simply supported rectangular plates with constant thickness consisting of a transversely isotropic linearly elastic material subjected to an arbitrary static load is presented. The governing partial differential equations for the potential functions are solved through the use of the Fourier method, which results in exponential and trigonometric expression along the plate thickness and the other two lengths respectively. The displacements, stresses, and internal forces are determined through the potential functions at any point of the body. To prove the validity of this approach, the analytical solutions developed in this paper are degenerated for the simpler case of plates containing isotropic material and compared with the existing solution. In addition, the numerical results obtained from this study are compared with those reported in other researches for the isotropic material, where excellent agreement is achieved for both thin and thick plates. The results show that increasing the thickness ratios of the plate causes compressive axial forces and central shear forces inside the plate. Finally, the internal forces and displacement components are calculated numerically for several kinds of transversely isotropic materials with different anisotropies and are compared with a finite element (FE) solution obtained from the ANSYS software, where the high accuracy of the present method is demonstrated. The effects of the material anisotropy are clearly revealed in the numerical results presented.

scholarly journals A Note on Full-Rank Factorization of Matrix

2019 ◽  
Vol 15 (2) ◽  
pp. 152-154
Author(s):  
Gyan Bahadur Thapa ◽  
J. López-Bonilla ◽  
R. López-Vázquez
Keyword(s):  
Singular Value Decomposition ◽  
Full Rank ◽  
Singular Value ◽  
The Matrix ◽  
Rank Factorization ◽  
Value Decomposition

We exhibit that the Singular Value Decomposition of a matrix Anxm implies a natural full-rank factorization of the matrix.

Mechanics of NiTi Reinforced Self-Healing Materials Producing Crack Closing Loads

2017 ◽  
Author(s):  
Nathan Salowitz ◽  
Ameralys Correa ◽  
Afsaneh Moghadam
Keyword(s):  
Shape Memory ◽  
Paradigm Shift ◽  
Fiber Composite ◽  
Self Healing ◽  
New Approach ◽  
The Matrix ◽  
Composite Form ◽  
External Loads ◽  
Shape Memory Fibers ◽  
Structural Matrix

Self-healing material structures with the inherent capability to mend damage will lead to a paradigm shift in design as fracture may no longer constitute a failure. Generally, there are two techniques of self-healing that operate at different scales, require different approaches and often are dealt with separately; geometric restoration and crack filling/bonding. Geometric restoration uses shape memory materials that can mechanically close fractures after they occur. Crack filling and bonding fills and chemically bonds fractured parts in place. Materials capable of recovering from complete fractures, that have propagated across the entire component, have typically taken a sparse fiber composite form with a structural matrix encapsulating shape memory fibers. This form of self-healing material has demonstrated the ability recover original bulk geometry. However, lacking bonding, the healed structures have not had the ability to resist subsequent externally applied loads without re-opening the crack. A new approach of pre-straining the shape memory fibers before curing them in a matrix in the pre-strained state is presented in this paper with basic theory and experimental results. Pre-straining the shape memory fibers before casting them in the matrix causes them to undergo constrained recovery upon activation. Thus, the samples create closing loads across the crack which are capable of withstanding external loads without re-opening.

Soil Parameter Identification Based on Field Monitoring Value of Displacement and Stress in Pit Retaining Structure

2011 ◽  
Vol 90-93 ◽  
pp. 323-327
Author(s):  
Fei Wang ◽  
Jian Xue Song
Keyword(s):  
Yellow River ◽  
Structure Design ◽  
Soil Reaction ◽  
Equilibrium Equations ◽  
Steel Pipes ◽  
Retaining Structure ◽  
Axial Forces ◽  
Reinforced Concrete Piles ◽  
Internal Bracing ◽  
Set Up

Parameter-M is the proportion factor of horizontal soil reaction when the soil is compressed horizontally, and the corresponding method of pit retaining structure analysis is named as M-method. M-method is widely used to determine the working state of pit retaining structures in China, however, parameter-M varies significantly when deduced by different approaches. An analysis unit is chosen in the subway station pit in Zhengzhou, center of China, on the bank of Yellow River. The retaining structure consists of reinforced concrete piles, internal bracing struts made of steel pipes. The horizontal displacements of retaining piles and the axial forces in pipe bracing struts are monitored in-situ. Then, calculation assumption is taken as that during the elastic deformation stage, parameter-M for each soil keeps constant. Then a series of equilibrium equations of forces acting on retaining structure are set up to determine the values of M for each soil corresponding to deferent stages of excavation. When the identified values of M are applied in the later projects, it shows the validity and accuracy of the method. Precise values of M are applied in the similar geological sites to optimize the retaining structure design.

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