Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Chance of psychiatric morbidity amongst recently diagnosed cancer outpatients attending a chemotherapy unit

The prevalent rate of psychiatry morbidity amongst patients with cancer reported in various studies ranges from 5 to 50%, a variation that can be attributed to differences in sample size, the disease itself and treatment factors. The objectives of the present study were to determine the frequency of psychiatric morbidity amongst recently diagnosed cancer outpatients and try to identify which factors might be related to further psychological distress. Two hundred and eleven (70.9%) female patients and 87 (29.1%) male patients from the chemotherapy unit of the Cancer Hospital A.C. Camargo (São Paulo) completed a questionnaire that featured data on demographic, medical and treatment details. The Self Reporting Questionnaire (SRQ-20) was administered to the patients to determine their personal psychiatric morbidity. Seventy-two patients (25.8%) scored > or = 8 in the SRQ-20, the cut-off point for a patient to be considered a psychiatric case. When the low and high scoring groups were compared no differences were detected regarding age, marital status, tumor site, sex, or previous treatment. Nonetheless, patients in the lowest social class and those who were bedridden less than 50% of the time had a significantly higher probability of being a psychiatric case. Regarding help-seeking behavior in situations in which they had doubts or were frightened, about 64% of the total sample did not seek any type of support and did not talk to anyone. This frequency of psychiatric morbidity agrees with data from the cancer literature. According to many investigators, the early detection of a comorbid psychiatric disorder is crucial to relieve a patient's suffering.