Manssour H. Moeinzadeh

Two-dimensional dynamic modelling of human knee joint

A mathematical dynamic model of the two-dimensional representation of the knee joint is presented. The profiles of the joint surfaces are determined from X-ray films and they are represented by polynomials. The joint ligaments are modelled as nonlinear elastic springs of realistic stiffness properties. Nonlinear equations of motion coupled with nonlinear constraint conditions are solved numerically. Time derivatives are approximated by Newmark difference formulae and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads are applied to the center of mass of the tibia and the ensuing motion is investigated. Numerical results on ligament forces, contact point locations between femur and tibia, and the orientation of tibia relative to femur are presented. The results are shown to be consistent with the anatomy of the knee joint.

A fiber-ceramic matrix composite material model for osteonal cortical bone fracture micromechanics: Solution of arbitrary microcracks interaction

Microcracks formed in bone are due to fatigue and cyclic loading. This formation is associated with a reduction of bone resistance to fracture. However, the significance of the parameters that govern microcrack behavior is not yet fully explored. A two-dimensional micromechanical fiber-ceramic matrix composite material model of the osteonal cortical bone is presented in this paper. The solution for the edge dislocations as Greens function, is adopted to formulate a system of singular integral equations for the general microcracks in vicinity of the osteon. The effects of microstructural morphology and heterogeneity of the bone upon the fracture behavior is investigated by computing the Stress Intensity Factor (SIF) near the microcracks tips. Analysis of microcracks interaction indicates the significance of microcracks configuration in the shape of either stress amplification or stress shielding.

Response of a two-dimensional dynamic model of the human knee to the externally applied forces and moments

This paper is concerned with response of a two-dimensional dynamic model of the human knee to the externally applied forces and moments. The profiles of the articulating surfaces of a normal knee joint are determined from X-ray films and they are represented by polynomials. Ligaments of the joint are modelled as nonlinear elastic springs of realistic stiffness properties. Nonlinear equations of motion, coupled with nonlinear constraint conditions, are solved numerically. Time derivatives are approximated by Newmark difference formulae and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads (force and moment) are applied to the tibia and subsequent motion is investigated. Results for the ligament and contact forces, contact point locations between femur and tibia and the corresponding dynamic orientation of tibia with respect to femur are presented.

Nonlinear finite element analysis of a frame stiffened with tension members

Abstract Finite element techniques were applied to the analysis of a general curved frame stiffened with tension members. Curved stiffened frames are found in a variety of structures such as space structures and cable roof structures. A tennis racket was used as a specific example problem. The model discussed here has the flexibility to deal with any frame shape and stringing pattern. The strings of the structure are modeled using nonlinear cable theory. The frame is modeled with linear isoparametric elements. Group iteration is used to analyze the two substructures, resulting in displacements, forces, and stresses for the entire structure.