Application of the Generalized Reduced Gradient Method in Mechanical Optimization Design

This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The algo- rithm of the GRG method is realized in Vissim software. Based on the mathematical model of the single-stage cylin- drical gear reducer, the simulation structure of the optimization design was achieved. The experiment results show that the GRG method has fewer iterations and higher precision. The GRG method is very suitable for solving mechanical optimization design.

Reduced projection augmented Lagrange bi-conjugate gradient method for contact and impact problems

Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.

A GENERAL TECHNIQUE FOR DEALING WITH DEGENERACY IN REDUCED GRADIENT METHODS FOR LINEARLY CONSTRAINED NONLINEAR PROGRAMMING

In this paper we discuss the degeneracy in nonlinear programming with linear constraints, and give a technique for dealing with degeneracy in a general model of reduced gradient algorithms. Under the assumption that the objective function is continuously differentiable, we prove that either the iterative sequence {xk} generated by the method terminates at a Kuhn-Tucker point after a finite number of iterations, or any cluster point of the sequence {xk} is a KuhnTucker point.

Extractive desulfurization of model fuels with a nitrogen-containing heterocyclic ionic liquid

A nitrogen-containing ionic liquid was synthesized using an aromatic nitrogen-containing heterocyclic and an amino acid,and applied to the extractive desulfurization process to remove benzothiophene,dibenzothiophene,and 4,6-dimethyldibenzothiphene from a model fuel oil.Chemical characterizations and simulation using Gaussian 09 software confirmed the rationality of an ionic liquid structure.Classification of non-covalent interactions between the ionic liquid and the three sulfur-containing contaminants was studied by reduced density gradient analysis.The viscosity of the ionic liquid was adjusted by addition of polyethylene glycol.Under extraction conditions of the volume of ionic liquid to oil as 1:1 and temperature as room temperature,the desulfurization selectivity of ionic liquid followed the order of 4,6-dimethyldibenzothiphene(15 min)<benzothiophene(15 min)≈dibenzothiophene(10 min).Addition of p-xylene and cyclohexene to the fuel oil had little effect.The extractant remained stable and effective after multiple regeneration cycles.