Applied mechanics

Engineering problems are generally tackled with applied mechanics through the application of theories of classical mechanics and fluid mechanics. Research in applied mechanics can be directly linked to biomedical engineering areas of interest like orthopaedics; biomechanics; human body motion analysis; soft tissue modelling of muscles, tendons, ligaments, and cartilage; biofluid mechanics; and dynamic systems, performance enhancement, and optimal control. == Brief history ==

The first science with a theoretical foundation based in mathematics was mechanics; the underlying principles of mechanics were first delineated by Isaac Newton in his 1687 book Philosophiæ Naturalis Principia Mathematica The first seminal work on applied mechanics to be published in English was A Manual of Applied Mechanics in 1858 by English mechanical engineer William Rankine. August Föppl, a German mechanical engineer and professor, published Vorlesungen über technische Mechanik in 1898 in which he introduced calculus to the study of applied mechanics. Timoshenko authored thirteen textbooks in applied mechanics, many considered the gold standard in their fields; he also founded the Applied Mechanics Division of the American Society of Mechanical Engineers in 1927 and is considered “America’s Father of Engineering Mechanics.” In 1930 Theodore von Kármán left Germany and became the first director of the Aeronautical Laboratory at the California Institute of Technology; von Kármán would later co-found the Jet Propulsion Laboratory in 1944. With the leadership of Timoshenko and von Kármán, the influx of talent from Europe, and the rapid growth of the aeronautical and defense industries, applied mechanics became a mature discipline in the U.S. by 1950. == Branches ==

Dynamics Dynamics, the study of the motion and movement of various objects, can be further divided into two branches, kinematics and kinetics. For classical mechanics, kinematics would be the analysis of moving bodies using time, velocities, displacement, and acceleration. Kinetics would be the study of moving bodies through the lens of the effects of forces and masses. In the context of fluid mechanics, fluid dynamics pertains to the flow and describing of the motion of various fluids. Statics The study of statics is the study and describing of bodies at rest. Static analysis in classical mechanics can be broken down into two categories, non-deformable bodies and deformable bodies. When studying non-deformable bodies, considerations relating to the forces acting on the rigid structures are analyzed. When studying deformable bodies, the examination of the structure and material strength is observed. In the context of fluid mechanics, the resting state of the pressure unaffected fluid is taken into account. == Relationship to classical mechanics ==

Applied Mechanics is a result of the practical applications of various engineering/mechanical disciplines; as illustrated in the table below. == Examples ==

Newtonian foundation Being one of the first sciences for which a systematic theoretical framework was developed, mechanics was spearheaded by Sir Isaac Newton's Principia (published in 1687). If the solid is to be weighed within the fluid, the fluid will be measured as lighter than the weight of the amount of fluid that was displaced by said solid. Further developed upon by proposition 5, if the solid is lighter than the fluid it is placed in, the solid will have to be forcibly immersed to be fully covered by the liquid. The weight of the amount of displaced fluids will then be equal to the weight of the solid. ==Major topics==

This section based on the "AMR Subject Classification Scheme" from the journal Applied Mechanics Reviews. Foundations and basic methods • Continuum mechanics • Finite element method • Finite difference method • Other computational methods • Experimental system analysis Dynamics and vibration • Dynamics (mechanics) • Kinematics • Vibrations of solids (basic) • Vibrations (structural elements) • Vibrations (structures) • Wave motion in solids • Impact on solids • Waves in incompressible fluids • Waves in compressible fluids • Solid fluid interactions • Astronautics (celestial and orbital mechanics) • Explosions and ballistics • Acoustics Automatic control • System theory and design • Optimal control system • System and control applications • Robotics • Manufacturing === Mechanics of solids === • Elasticity • Viscoelasticity • Plasticity and viscoplasticity • Composite material mechanics • Cables, rope, beams, etc • Plates, shells, membranes, etc • Structural stability (buckling, postbuckling) • Electromagneto solid mechanics • Soil mechanics (basic) • Soil mechanics (applied) • Rock mechanics • Material processing • Fracture and damage processes • Fracture and damage mechanics • Experimental stress analysis • Material Testing • Structures (basic) • Structures (ground) • Structures (ocean and coastal) • Structures (mobile) • Structures (containment) • Friction and wear • Machine elements • Machine design • Fastening and joining === Mechanics of fluids === • Rheology • Hydraulics • Incompressible flow • Compressible flow • Rarefied flow • Multiphase flow • Wall Layers (incl boundary layers) • Internal flow (pipe, channel, and couette) • Internal flow (inlets, nozzles, diffusers, and cascades) • Free shear layers (mixing layers, jets, wakes, cavities, and plumes)\ • Flow stability • Turbulence • Electromagneto fluid and plasma dynamics • Hydromechanics • Aerodynamics • Machinery fluid dynamics • Lubrication • Flow measurements and visualization === Thermal sciences === • Thermodynamics • Heat transfer (one phase convection) • Heat transfer (two phase convection) • Heat transfer (conduction) • Heat transfer (radiation and combined modes) • Heat transfer (devices and systems) • Thermodynamics of solids • Mass transfer (with and without heat transfer) • Combustion • Prime movers and propulsion systems === Earth sciences === • Micromeritics • Porous media • Geomechanics • Earthquake mechanics • Hydrology, oceanology, and meteorology === Energy systems and environment === • Fossil fuel systems • Nuclear systems • Geothermal systems • Solar energy systems • Wind energy systems • Ocean energy system • Energy distribution and storage • Environmental fluid mechanics • Hazardous waste containment and disposal === Biosciences === • Biomechanics • Human factor engineering • Rehabilitation engineering • Sports mechanics == Applications ==

• Electrical Engineering • Civil engineering • Mechanical Engineering • Nuclear engineering • Architectural engineering • Chemical engineering • Petroleum engineering == Publications ==

• Journal of Applied Mathematics and Mechanics • Newsletters of the Applied Mechanics Division • Journal of Applied Mechanics • Applied Mechanics Reviews • Applied Mechanics • Quarterly Journal of Mechanics and Applied Mathematics • Journal of Applied Mathematics and Mechanics (PMM) • Gesellschaft für Angewandte Mathematik und Mechanik • Acta Mechanica Sinica ==See also==