Calculation of the Collapsing Critical Load of a Translating Cam Mechanism and Roller Translating Follower Actuating an Elevator

The above-ground parking lot above Dâmbovița river has stemmed from the need to cover the lack of parking lots in Bucharest. The parking lot may be serviced, in case of emergency, by auxiliary elevators that are operated by mechanisms provided with translating cams and roller translating followers. In this paper, a calculation of the collapsing critical load shall be performed. One shall also analyze here the rod model and the model with several rods of the mechanism provided with a translating cam and roller translating follower. In order for the rods to resist collapsing, one must be found in the elastic field, thus verifying Euler’s formula.

Path Analysis for Hybrid Rigid–Flexible Mechanisms

Hybrid rigid–flexible mechanisms are a type of compliant mechanism that combines rigid and flexible elements, being that their mobility is due to rigid-body joints and the relative flexibility of bendable rods. Two of the modeling methods of flexible rods are the Cosserat rod model and its simplification, the Kirchhoff rod model. Both of them present a system of differential equations that must be solved in conjunction with the boundary constraints of the rod, leading to a boundary value problem (BVP). In this work, two methods to solve this BVP are applied to analyze the influence of external loads in the movement of hybrid compliant mechanisms. First, a shooting method (SM) is used to integrate directly the shape of the flexible rod and the forces that appear in it. Then, an integration with elliptic integrals (EI) is carried out to solve the workspace of the compliant element, considering its buckling mode. Applying both methods, an algorithm that obtains the locus of all possible trajectories of the mechanism’s coupler point, and detects the buckling mode change, is developed. This algorithm also allows calculating all possible circuits of the mechanism. Thus, the performance of this method within the path analysis of mechanisms is demonstrated.

On a nonlinear rod exhibiting only axial and bending deformations: mathematical modeling and numerical implementation

In this work, we present the mathematical formulation and the numerical implementation of a new model for initially straight, transversely isotropic rods. By adopting a configuration space that intrinsically avoids shear deformations and by systemically neglecting the energetic contribution due to torsion, the proposed model admits an unconstrained variational statement. Moreover, as the natural state of the rod is the trivial one and the mechanical properties are homogeneous on the cross section, the need for pull-back and push-forward operations in the formulation is totally circumvented. These features impose, however, some smoothness requirements on the stored energy function that need to be carefully considered when adopting general constitutive models. In addition to introducing the rod model, we propose a spatial discretization with the finite element method, and a time integration with a hybrid, implicit scheme. To illustrate the favorable features of the new model, we provide results corresponding to numerical simulations for plane and three-dimensional problems that are investigated in the static and dynamic settings. Finally, and to put the presented ideas in a suitable context, we compare solutions obtained with the new model against a rod model that allows for torsion and shear.

Determining the mechanical characteristics of composite materials reinforced with woven preforms

Reduction of the complexity of production of articles from composite materials is largely ensured by the use of reinforcing semi-finished products in which fibers pre-form a framework. Among all the variety of reinforcing systems, woven sleeves (preforms) occupy a special place. The high degree of deformability in a nonimpregnated condition makes it possible to lay this reinforcement on any surface without folds and cuts that provide preservation of strand continuity. This advantage of woven sleeves is accompanied by a change in local reinforcement angles and, consequently, the variable nature of physical and mechanical characteristics of the curved part surface. A method for calculating physical and mechanical characteristics of the composite based on preforms at any point of the part depending on the pattern of laying strands on a curved surface has been developed. The possibility of application of the rod model of the composite to describe physical and mechanical characteristics of the composite material with a woven reinforcement was analyzed. The model essence consists in that the composite is modeled by a diamond-shaped rod system. The rhombus sides serve as fibers and the diagonals as the binder. To verify the theoretical results and substantiate practical recommendations, a series of experimental studies were performed based on the formation of material specimens from two types of woven sleeves with different reinforcement angles. The experimental study program included tensile, bending, and compression tests. A fairly good convergence of theoretical and experimental data was obtained. For example, a square of the correlation coefficient was not less than 0.95 for the modulus of elasticity, not less than 0.8 for the Poisson's ratio, and not less than 0.9 for tensile and compressive strengths. This is the rationale for using the rod model to describe the considered class of composites. The use of the developed procedure will make it possible to increase the perfection of the considered class of designs and obtain rational parameters of the process of their manufacture.