Abstract . Rod structures are widely used in mechanical
engineering as connecting and transmission links for structural elements
of a wide variety of machines and mechanisms. During operation, they are
subjected to variable mechanical and thermal influences, which create a
complex stress-strain state in structural elements, depending on their
temperature, and affecting their strength and reliability. Therefore,
the determination of the thermally stressed state of rod structures,
taking into account their mechanical properties (in particular,
elasticity and thermal conductivity) is one of the topical scientific
and technical problems.
Here, spatially one-dimensional unsteady boundary value problems (BVPs)
of uncoupled thermoelasticity are considered, which can be used to study
various bar structures. This model describes well thermodynamic
processes at low strain rates and here a unified technique is proposed
for solving various BVPs typical of practical applications.
Problems of determining the thermally stressed state of a thermoelastic
rod using a model of uncoupled thermoelasticity are considered.
Generalized solutions of non-stationary and stationary direct and
semi-inverse BVPs under the action of power and heat sources of various
types are constructed on the basis of the method of generalized
functions. Acting sources can also be specified by singular generalized
functions, under different boundary conditions at the ends of the rod.
Considered are shock elastic waves that arise in such structures under
the action of shock loads. Regular integral representations of
generalized solutions are obtained, which give an analytical solution to
the stated BVPs.
Key words: thermoelastic rod, boundary value problems,
method of generalized funсtions.