scholarly journals Mathematical Programming and Integro-Differential Equations

1965 ◽  
Vol 2 (1) ◽  
pp. 171-202 ◽  
Author(s):  
Wayne T. Ford
Keyword(s):  
Mathematical Programming ◽  
Differential Equations

scholarly journals Studies on Static Frictional Contact Problems of Double Cantilever Beam Based on SBFEM

2017 ◽  
Vol 11 (1) ◽  
pp. 896-905
Author(s):  
Zhu Chaolei ◽  
Gao Qian ◽  
Hu Zhiqiang ◽  
Lin Gao ◽  
Lu Jingzhou
Keyword(s):  
Mathematical Programming ◽  
Differential Equations ◽  
Cantilever Beam ◽  
Frictional Contact ◽  
Double Cantilever Beam ◽  
Contact Problems ◽  
Contact Forces ◽  
Contact Conditions ◽  
Good Convergence ◽  
Practical Engineering

Introduction: The frictional contact problem is one of the most important and challenging topics in solids mechanics, and often encountered in the practical engineering. Method: The nonlinearity and non-smooth properties result in that the convergent solutions can't be obtained by the widely used trial-error iteration method. Mathematical Programming which has good convergence properties and rigorous mathematical foundation is an effective alternative solution method, in which, the frictional contact conditions can be expressed as Non-smooth Equations, B-differential equations, Nonlinear Complementary Problem, etc. Result: In this paper, static frictional contact problems of double cantilever beam are analyzed by Mathematical Programming in the framework of Scaled Boundary Finite Element Method (SBFEM), in which the contact conditions can be expressed as the B-differential Equations. Conclusion The contact forces and the deformation with different friction factors are solved and compared with those obtained by ANSYS, by which the accuracy of solving contact problems by SBFEM and B-differential Equations is validated.

Application of Double Side Approach Method to the Solution of Fully Developed Laminar Flow in Duct Problems

2013 ◽  
Vol 29 (3) ◽  
pp. 471-479
Author(s):  
H.-W. Tang ◽  
Y.-T. Yang ◽  
C.-K. Chen
Keyword(s):  
Maximum Principle ◽  
Mathematical Programming ◽  
Laminar Flow ◽  
Differential Equations ◽  
Slip Boundary Condition ◽  
Optimization Method ◽  
The Maximum Principle ◽  
Weighted Residuals ◽  
Slip Boundary ◽  
Approach Method

AbstractThe double side approach method combines the method of weighted residuals (MWR) with mathematical programming to solve the differential equations. Once the differential equation is proved to satisfy the maximum principle, collocation method and mathematical programming are used to transfer the problem into a bilateral inequality. By utilizing Genetic Algorithms optimization method, the maximum and minimum solutions which satisfy the inequality can be found. Adopting this method, quite less computer memory and time are needed than those required for finite element method.In this paper, the incompressible-Newtonian, fully-developed, steady-state laminar flow in equilateral triangular, rectangular, elliptical and super-elliptical ducts is studied. Based on the maximum principle of differential equations, the monotonicity of the Laplace operator can be proved and the double side approach method can be applied. Different kinds of trial functions are constructed to meet the no-slip boundary condition, and it was demonstrated that the results are in great agreement with the analytical solutions or the formerly presented works. The efficiency, accuracy, and simplicity of the double side approach method are fully illustrated in the present study to indicate that the method is powerful for solving boundary value problems.

scholarly journals Cultural Challenge: Teaching Mathematics to Non-mathematicians

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Andrijana Burazin ◽  
Veselin Jungic ◽  
Miroslav Lovric
Keyword(s):  
Mathematical Programming ◽  
Differential Equations ◽  
Linear Algebra ◽  
Mathematical Reasoning ◽  
Discrete Mathematics ◽  
Teaching Mathematics ◽  
Mathematics Majors ◽  
Curricular Design ◽  
Learning Mathematics ◽  
Authentic Problems

A “mathematics for non-mathematicians” course, commonly known as a “service” course is an undergraduate mathematics course developed for students who are not (going to become) mathematics majors. Besides calculus, such courses may include linear algebra, mathematical reasoning, differential equations, mathematical programming and modeling, discrete mathematics, mathematics for teachers, and so on. In this article we argue that a good, productive curricular design and teaching of service courses happen through a meaningful collaboration between a mathematics instructor and the department whose students are taking the course. This collaboration ensures that “non-mathematicians” see the relevance of learning mathematics for their discipline (say, by discussing authentic problems and examples), but also appreciate the relevance and benefits which mathematics brings to their overall education and skills set.

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