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Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an ...
For two-dimensional, plane strain problems the strain-displacement relations are = ; = [+] ; = Repeated differentiation of these relations, in order to remove the displacements and , gives us the two-dimensional compatibility condition for strains
The problem is in #P, the class of problems that can be defined as counting the number of accepting paths of a polynomial-time non-deterministic Turing machine. The problem is #P-hard, meaning that every other problem in #P has a Turing reduction or polynomial-time counting reduction to it. A counting reduction is a pair of polynomial-time ...
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
Descriptively, a statically determinate structure can be defined as a structure where, if it is possible to find internal actions in equilibrium with external loads, those internal actions are unique. The structure has no possible states of self-stress, i.e. internal forces in equilibrium with zero external loads are not possible.
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, [1] chemistry, neuroscience, [2] computer science, [3] [4] information theory [5] and ...
The MAX-SAT problem is OptP-complete, [1] and thus NP-hard, since its solution easily leads to the solution of the boolean satisfiability problem, which is NP-complete. It is also difficult to find an approximate solution of the problem, that satisfies a number of clauses within a guaranteed approximation ratio of the optimal solution.
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).