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The equilibrium governing equations of nonlocal anisotropic thin-walled circular cylindrical shell under combined axial compressive force, torsional load, and external pressure are explicitly derived. This is accomplished by appropriately combining the equilibrium equations and the strain-displacement relations according to Flugge’s shell theory and the stress-stain equations of Eringen’s nonlocal elasticity theory. An analytical solution for the buckling of the shells is presented by using the complex method. This model is validated by a good agreement between the results given by the present model and available data in the literature. Furthermore, the model is utilized to elucidate the buckling properties for different load combinations.

Torsional resistance of a single prestressing tendon was derived on the basis of the theorem of virtual work to control the torsional rotation by nonequal prestressing forces on both sides of the webs of a flexural member. The energy formulation revealed that the vertical component of the prestressing force has a significant role in resisting the torsional rotation, whereas the axial component is responsible for the warping-related stiffness. The most influential location of the prestressing tendon was the point where the value of the warping function is maximized. The resulting finite-element equilibrium equations yielded nodal forces at the degrees of freedom corresponding to torsion and warping. Through numerical applications, it was suggested that the conventional solution method of beam finite-element formulation on the basis of the transformed cross section can be improved by adopting the nodal forces derived in this paper. Further, it was shown that the torsional rotation can be controlled ...

When a prestressed double-T beam is subjected to torsion, a pair of prestressing tendons resists torsional rotation because of the restoring action of the displaced prestressing tendons. A comprehensive formulation to account for the torsional restoring action of double-T beams is presented, based on Vlasov’s hypothesis of considering warping displacement in an open-section. The deformation energies of prestressing tendons and reinforcing bars are calculated based on the deformed geometry to obtain the total potential energy. A two-noded beam element with seven degrees of freedom per node approximates an axial displacement, two translations, two flexural, and one torsional rotations, and a warping displacement to derive the finite-element equilibrium equations by minimizing the potential energy function. The role of prestressing forces of the tendons on the torsional resistance and the limitations of the traditional transformed section approach are addressed when it is applied to torsional problems. As a ...

The objective of this paper is to present the feasibility of applying Vlasov's theory of thin walled bars to model the behavior of rib-reinforced cantilevered plates. A simple analytical model based on Vlasov's theory is presented and validated against experimental results. It is shown that the presented theoretical method is simple and sufficiently accurate to be used as a design tool. The presented approach is also valid for plates fabricated from composite materials.

Buckling of rectangular plates under uniaxial loading is considered. The plates are uniform and elastic, and the load is uniform. The unloaded edges are simply supported, whereas the loaded edges have no out‐of‐plane deflection and are elastically restrained against rotation. Based on observations reported in the literature, this rotational resistance may increase as the plate is compressed. To take this stiffening behavior into account, the rotational stiffness at the loaded edges is assumed to be a linear function of the load. The equilibrium equation is solved analytically, leading to two characteristic equations. One corresponds to buckling modes that are symmetric in the direction of loading, and the other to antisymmetric modes. Critical loads are computed and plotted as a function of the aspect ratio for various cases. Results for load‐dependent conditions are compared to those for loaded edges that are simply supported, clamped, or elastically restrained with load‐independent stiffness. It is foun...

Post‐buckling equilibrium paths of complex, elastic, hyperstatic, pin‐jointed lattices composed of slender members are studied under the aspect of finite deformation using a new simplified theory, which is presented in matrix formulation. A general numerical procedure is developed on a digital computer for the solution of the reduced equilibrium equations and the kinematic admissibility conditions admitting post‐buckling equilibrium modes. A method for a direct evaluation of the most degrading mode based on the solution of a quadratic minimization problem, subject to linear constraints, is also presented. The procedure is illustrated on the lattice of a model reticulated shell of a 40 ft base diameter, designed and optimized to carry a head of some 420 ft of sea water. The effect of initial geometrical imperfections on the post‐buckling paths is analyzed by means of an imperfection‐sensitivity parameters. The method permits an estimation of the load‐displacement curves of the imperfect lattice, if the pat...

An elasticity solution for sandwich plates assembled with nonrigid bondings is presented. The solution satisfies the equilibrium equations of the face and core elements, the compatibility equations of stresses and strains at the interfaces, and the relevant boundary conditions. To investigate the effects of bonding stiffnesses on the responses of sandwich plates, numerical evaluations are conducted. The results obtained have shown that the bonding stiffness, up to a certain level, has a strong effect on the plate deflection. Beyond this level, the usual assumption of perfect bonding used in classical theories is quite acceptable. An answer to what constitutes “perfect” bonding is found in terms of the ratio of the core stiffness to the bonding stiffness.

In some geometrically nonlinear problems, the effects of external loads are altered significantly by the deformations of structures themselves. In finite element analysis, the assumed displacement method is often used to solve this category of problems. But the formulations involve a huge number of unsymmetric matrices in the equilibrium equations and become extremely complex. An efficient algorithm is presented such that only a minimum number of symmetric, differentiation‐invariant, repeatable matrices are required in the entire formulation.