Engineering

In the field of analysis of structures, it is often desired to calculate the dynamic response of a structure subjected to general dynamic excitation. In order to achieve the calculation of the response, usually numerical integration schemes are applied. In most cases the structure is also discretized by the finite element method resulting in a dynamic system of differential equations, in matrix form with a large number of unknowns. Special numerical integration methods have been developed for these cases like the Linear Acceleration method, the Central Difference method, the HHT-α method...

Multibody analysis is the study of the dynamics of rigid or deformable bodies undergoing large displacements and rotations, interacting with each other via constraints such as joints or contact. Multibody analysis is used in a wide area of applications in engineering such as vehicles and aircraft, engines and transmission components, particle simulations such as grains, sand, molecules etc. robotics and other.

The basic concept of a multibody system is that each body has six (6) degrees of freedom (dof) and each contraint imposes some equations usually coupling some of the dofs...

Inertia relief is an effective technique for the analysis of structures without supports, often combined with the finite element method. A structure without supports basically exhibits a rigid body motion. In order to evalute the elastic behaviour of the structure and calculate stresses, strains etc. the rigid body motion must be eliminated from the structure. Simply put, the structure must be "relieved" of inertial effects in order for a static equilibrium to be established. Examples of such structures are aircrafts, launch vehicles, spacecrafts, marine structures, machine components etc...

The analysis of body in white (BIW) is an important analysis in the field of Noise, Vibration and Harshness (NVH) of a vehicle during its early design stage. A car BIW must meet certain NVH design criteria and also exhibit certain stiffness, strength and fatigue life. In a typical car manufacturing development cycle, the above procedure takes place in the engineering design phase and it is done with FE analysis. A car BIW is comprised only of the car body's sheet metal components that have been welded together, so any moving parts such as doors, hoods, lids, fenders, motor, suspension...

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In many practical engineering problems, the derived mathematical equations frequently end up in the formulation of some kind of eigenvalue problem.

Practical examples for the usage of eigenproblems include principal component analysis, rigid bodies principal axes and tensor of moment of inertia calculation, stress tensor calculation, stability analysis, vibration analysis, matrix diagonalization and other problems.

A typical example of the utilisation of the eigenvalue problem in practical engineering, is the caclulation of the fundamental frequencies and modes of a...

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The simple harmonic oscillator with bilinear restoring force is a typical model used for the analysis of the response of mechanical systems which include contact or impact between their components. Such mechanical systems exist in industrial machinery as well as in other mechanical systems such as vehicle suspension systems and other components. These problems are nonlinear due to the nature of the restoring force and under some conditions they can exhibit even discontinuities in the velocity and acceleration of the their response. For example in the case where the slope of the bilinear...

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