Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms.
This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.013J. In 2005, ocean engineering became part of Course 2 (Department of Mechanical Engineering), and this subject merged with 2.003.

This course introduces finite element methods for the analysis of solid, structural, fluid, field, and heat transfer problems. Steady-state, transient, and dynamic conditions are considered. Finite element methods and solution procedures for linear and nonlinear analyses are presented using largely physical arguments. The homework and a term project (for graduate students) involve use of the general purpose finite element analysis program ADINA. Applications include finite element analyses, modeling of problems, and interpretation of numerical results.

Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences. In these two video courses, Professor K. J. Bathe, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses the implementation of finite element procedures for linear and nonlinear analyses.
These videos were produced in 1982 and 1986 by the MIT Center for Advanced Engineering Study.

This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications.

After conducting the associated activity, students are introduced to the material behavior of elastic solids. Engineering stress and strain are defined and their importance in designing devices and systems is explained. How engineers measure, calculate and interpret properties of elastic materials is addressed. Students calculate stress, strain and modulus of elasticity, and learn about the typical engineering stress-strain diagram (graph) of an elastic material.

Overview of mechanical properties of ceramics, metals, and polymers, emphasizing the role of processing and microstructure in controlling these properties. Basic topics in mechanics of materials including: continuum stress and strain, truss forces, torsion of a circular shaft and beam bending. Design of engineering structures from a materials point of view.

The SEEING STRUCTURES video tutorials facilitate understanding of engineering mechanics (Statics, Mechanics of Materials, Structural Analysis, etc.). My objective is to share my work with the engineering education community. Please feel free to use my videos in your classroom, attributing me with: "Seeing Structures (Video Tutorials)© 2020-present by Susan Reynolds is licensed under CC BY-NC-SA 4.0"

1.050 is a sophomore-level engineering mechanics course, commonly labelled "Statics and Strength of Materials" or "Solid Mechanics I." This course introduces students to the fundamental principles and methods of structural mechanics. Topics covered include: static equilibrium, force resultants, support conditions, analysis of determinate planar structures (beams, trusses, frames), stresses and strains in structural elements, states of stress (shear, bending, torsion), statically indeterminate systems, displacements and deformations, introduction to matrix methods, elastic stability, and approximate methods. Design exercises are used to encourage creative student initiative and systems thinking.

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

Applies solid mechanics to analysis of high-technology structures. Structural design considerations. Review of three-dimensional elasticity theory; stress, strain, anisotropic materials, and heating effects. Two-dimensional plane stress and plane strain problems. Torsion theory for arbitrary sections. Bending of unsymmetrical section and mixed material beams. Bending, shear, and torsion of thin-wall shell beams. Buckling of columns and stability phenomena. Introduction to structural dynamics. Exercises in the design of general and aerospace structures.

This course provides a comprehensive introduction to crystalline structure, crystal chemistry, and bonding in rock-forming minerals. It introduces the theory relating crystal structure and crystal symmetry to physical properties such as refractive index, elastic modulus, and seismic velocity. It surveys the distribution of silicate, oxide, and metallic minerals in the interiors and on the surfaces of planets, and discusses the processes that led to their formation. It also addresses why diamonds are hard and why micas split into thin sheets.