TL;DR: In this paper, the amplitude of the dominant crack-tip singularity, as measured by the path-independent J-integral, and applied load, the load point displacement, and the crack opening displacement are derived for both incremental and deformation theories of plasticity.

TL;DR: In this article, a finite element formulation based on approximation in the Laplace transform space, is given for Biot's Consolidation theory and conditions under which these integration schemes are stable are investigated.

TL;DR: Using numerical integration in the formation of the finite element mass matrix and placing the movable nodes at integration points causes it to become lumped or diagonal (block diagonal) with the optimal rate of energy convergence retained.

TL;DR: In this paper, the constitutive equation for stress in a hyperelastic body undergoing nonisothermal deformation is derived from a free energy function, which is then decomposition into an isothermal, "effective" strain energy function and a function depending only on temperature.

TL;DR: In this paper, the authors apply the strain energy density failure criterion to plane notch problems, where the crack now becomes a special case of a more generalized approach to failure, and the specific case considered is that of the plane elliptical cavity under remote tension and compression.

TL;DR: In this paper, an integral equation method for the solution of axially symmetrical elasticity problems is presented for the treament of both simply and multiply connected regions with irregular boundary shapes and any boundary load distribution which satisfies the equilibrium conditions.

TL;DR: In this paper, a branched crack consisting of a main crack and a straight branch starting from one of its tip located in an infinite elastic sheet is considered under the assumptions of two-dimensional theory of Elasticity.

TL;DR: In this paper, the local character of the elastostatic field in plane strain near a point that separates a free from an adjoining fixed segment of a rectilinear boundary component is investigated.

TL;DR: In this paper, a curved-shell finite element of triangular shape is described which is based on conventional shell theory expressed in terms of surface coordinates and displacements Each of the three surface displacement components is independently represented by a two-dimensional polynomial of constrained-quintic order giving the element a total of 54 degrees of freedom.

TL;DR: In this article, a strain gradient theory of thermoelasticity is formulated employing a method due to Mindlin, and the basic equations for linear dynamical thermo-elasticities for infinitesimal motion are obtained and discussed.

TL;DR: In this paper, a quasi-analytical finite element procedure is developed which can obtain the frequency and buckling eigenvalues of prestressed rotating anisotropic shells of revolution, in addition to the usual centrifugal forces, the rotation effects treated also include the contribution of Coriolis forces.

TL;DR: In this paper, a correspondence between the Westergaard stress function for crack problems and a newly-introduced Westergaard function for rigid line inclusion problems has been shown, and a scheme is presented to modify these rigid-inclusion solutions to account approximately for non-zero compliance of real fibers in a composite material.

TL;DR: In this article, a general solution of the plane problem of a finite number of co-linear cracks in an anisotropic material is presented by reducing the problem to four very simple Riemann-Hilbert problems.

TL;DR: In this article, the lateral buckling equation was developed for a uniform, slender cantilever beam with a load applied at the shear center of the end cross section. But the error resulted from a failure to properly distinguish between the geometric and elastic angles of twist, resulting in a buckling load formula noticeably different from formulas based on these earlier equations.

TL;DR: In this article, the problem of the free vibrations of a rectangular elastic plate, either clamped or simply supported, with a central circular hole has been investigated by a least-squares point-matching method.

TL;DR: In this paper, the authors present a method to deal with an inclined crack in an elastic strip, which involves the solutions for a cracked plane and an uncracked strip and results in two coupled singular integral equations with finite interval of integration.

TL;DR: In this paper, the shakedown problem for a composite lamina made of an elastic-plastic matrix and elastic cylindrical fibers is studied, and it is concluded that significant shakedown effects can be caused only by the I 1 = 1/2(T 11 + T 22 ) and I 2 = T 33 components of the remotely applied stress field which are symmetric about the axis x 3 of the fiber; T 11 and T 22 are the normal composite stresses in the transverse plane.

TL;DR: In this paper, an analytical and a matrix displacement approach is used to obtain a load-deflection relationship of columns made of a material which can resist little or no tension, and a rigorous solution is presented along with an approximate finite element method involving an incremental, step-by-step approach.

TL;DR: In this article, the dispersive properties of elastic waveguides of arbitrary cross-section were analyzed using the finite element theory for the analysis of frequency spectra of fiber reinforced composite.

TL;DR: In this paper, the authors derived the nominal stress rate for an elastic-plastic material with an intermediate relaxed configuration from a potential function expressed in terms of the gradient of the displacement rate.

TL;DR: In this paper, the authors considered the elastodynamic problem of diffraction of stress waves by a crack near an interface and reduced the case of a crack perpendicular to the interface to a system of singular integral equation.

TL;DR: In this article, the buckling due to axial compression was investigated for elastic-plastic, stiffened wide panels either continuous in the longitudinal direction over several transverse supports or finite and supported along the two edges.

TL;DR: In this article, it is shown that loading surfaces must exist for a plastic material as a result of Caratheodory's theorem on Pfaffian forms, and that a yield hypersurface in state space may be defined as the boundary of the region in which no loading surfaces exist (the elastic region) if this region has a positive volume, otherwise this region degenerates into the quasi-yield hypersurfaces.

TL;DR: In this paper, a general analytical and numerical procedure based on the linear theory is outlined for the elastic stress and deflection analysis of an arbitrary plane curved beam subjected to arbitrary static and dynamic loads.

TL;DR: In this paper, the problem of center-cracked strip subjected to uniform remote anti-plane shear stress is transformed to a problem in a hodograph plane which is solved exactly by Mellin transform and Wiener-Hopf technique.

TL;DR: In this paper, the Lax-Wendroff method was used to calculate the critical time for the elastic rod shock and acceleration wave in isotropic, incompressible, hyperelastic solids.

TL;DR: In this paper, an elastodynamic explanation of running crack bifurcation is explored, where a semi-infinite body in a state of antiplane strain is assumed to contain a two-dimensional edge crack, and a quasi-static increase of external loads gives rise to rapid crack propagation at time t = 0, with an arbitrary and time-varying speed, but in the plane of the crack.