On a class of solutions of algebraic homogeneous linear equations

1967 ◽  
Vol 18 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Á. Pethő
Keyword(s):  
Linear Equations ◽  
Homogeneous Linear

A New Algorithm for Calculating the Degrees of Freedom of Complex Mechanisms

2011 ◽  
Vol 346 ◽  
pp. 324-331
Author(s):  
Wei Jiang ◽  
Xin Luo ◽  
Wen Chuan Jia ◽  
Yuan Tai Hu ◽  
Hong Ping Hu
Keyword(s):  
Degrees Of Freedom ◽  
Linear Equations ◽  
Linear Constraint ◽  
Coefficient Matrix ◽  
Constraint Matrix ◽  
Constraint Equations ◽  
Complex Mechanisms ◽  
Traditional Approaches ◽  
Homogeneous Linear

A new algorithm is presented to calculate the degrees of freedom (DOFs) of spatial complex mechanisms by using the coefficient matrix of the linear constraint equations. A joint constraint matrix is firstly put forward for each kind of joint to formulate linear constraint equations in terms of spatial fine displacements of joint acting point with respect to joint frame. Two kinds of transformation are then proposed to rewrite all the constraint equations in terms of a set of fine displacements of all bodies and it leads to a set of homogeneous linear equations. The rank of the resulting coefficient matrix stands for the number of effective constraints and therefore the DOFs of the mechanism can be easily figured out. The proposed method can be widely used to solve the problem of DOFs for many spatial complex mechanisms, which may not be correctly solved with traditional approaches. Besides, the proposed method is very easy for implementation.

scholarly journals On the Solubility of Linear Algebraic Equations (Contd.)

1913 ◽  
Vol 12 ◽  
pp. 137-138
Author(s):  
John Dougall
Keyword(s):  
Linear Equations ◽  
Homogeneous System ◽  
Algebraic Equations ◽  
Similar Reasoning ◽  
Null Solution ◽  
Linear Algebraic Equations ◽  
The Given ◽  
Homogeneous Linear

A system of n non-homogeneous linear equations in n variables has one and only one solution if the homogeneous system obtained from the given system by putting all the constant terms equal to zero has no solution except the null solution.This may be proved independently by similar reasoning to that given for Theorem I., or it may be deduced from that theorem. We follow the latter method.

The Influence of First Order Shear Deformation on Dynamic Buckling of Composite Bar

2015 ◽  
Vol 751 ◽  
pp. 195-199 ◽  
Author(s):  
Long Fei Wang ◽  
Zhi Jun Han ◽  
Xiao Peng Yan ◽  
Guo Yun Lu
Keyword(s):  
Shear Deformation ◽  
Linear Equations ◽  
Shear Deformation Theory ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Stress Wave Propagation ◽  
Critical Buckling Load ◽  
First Order ◽  
Homogeneous Linear ◽  
Reddy Theory

Taking stress wave propagation into account, the governing equations of composite bar with the clamped-fixed boundary conditions considering FSDT (first order shear deformation theory) are derived on the basis of Reddy’ theory and solved by the variable-separated method. The analytic expression of the critical buckling load is obtained basing on the characteristics of homogeneous linear equations having nonzero-solution. The results of the theoretical study and the numerical calculation indicate that FSDT has influence on dynamic buckling of composite bar, and the critical buckling load is small when FSDT is considered. They also show that the magnitude of effect taken by FSDT is small when the layer angle is big.

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