Search Results (11)

The current engineering theories on bending vibrations and the stability of beam structures are based on solving eigenvalue problems through similarly formulated differential equations. Solving the eigenvalue problem for engineering calculations is particularly laborious, especially for non-classical supports, where factors like the stiffness of supports, axial forces, or temperature must be considered. In this case, the solution can be obtained only by numerical methods using specially created programs, which makes it difficult to select supports for a given planar beam structure in engineering practice. This work utilizes established solutions from eigenvalue problems in the theory of vibrations and stability of beams, incorporating factors such as axial forces, temperature, and support stiffness. This combined solution is applicable to beam structures of any type and cross-section, as it is determined solely by the selected support conditions (stiffness) and loading (axial force, temperature). Approximation of eigenvalue problem solutions through continuous functions allows the readers to use them for the analytical solution of the design problem of choosing a support system to ensure the frequency of vibrations and stability of the planar beam structure. At the same time, the known solutions given in the reference books on bending vibrations and stability become their particular solutions. This approach is applicable to solving problems of vibrations and loss of stability of various types (torsional, longitudinal, etc.), and is also applicable in other disciplines where solving problems for eigenvalues is required. Full article

In order to enhance the accuracy of calculations for four-node quadrilateral shell elements, modifications have to be made to the computation of the membrane strain rate and transverse shear strain rate. For membrane strain rate calculations, the interpolation of the quadratic displacement of the nodes along the edges of the quadrilateral shell element is implemented, along with the introduction of a degree of freedom for rotation around the normal. Additionally, the elimination of the zero-energy mode of additional stiffness is achieved through a penalty function. When computing the transverse shear strain rate, the covariant component is expressed in the tensor of the natural coordinate system, followed by the elimination of shear self-locking in the element coordinate system. The strain-updating calculation and stress-updating calculation for the quadrilateral shell element, utilizing the model and J2 flow theory, respectively, are suitable for small deformations, geometric nonlinearity, and elastic–plastic problems. The improved quadrilateral shell element successfully undergoes in-plane and bending fragment inspections, demonstrating good reliability and calculation accuracy for the dynamic analysis of planar shells, curved shells, and twisted shells. Full article

For wide flange box sections, conventional Euler–Bernoulli beam theory with maintaining the cross-section planarity may lead to underestimation of axial stresses. Axial stresses in cross-section flanges may have a non-uniform distribution due to shear pliability, decreasing in value from the flange–web junction to the middle area of the flange. This phenomenon leads to the introduction of an effective flange width with a uniform distribution of original maximum stress. Furthermore, the introduction of flange curvature makes it even more complex due to the varying lever arm of each flange part with respect to the neutral bending axis. Because of this, in some cases, it is hard to predict where the flange’s highest normal stress value will appear. In this paper, the shear lag effect on wide curved box sections is analyzed through parametric numerical analysis using the FEA software Dlubal RFEM 5, together with visual programming performed in Rhino Grasshopper. This study investigates the interaction of the shear lag effect and plane section hypothesis, which can be simplistically represented as a reduction in the impact of shear lag and the activation of a larger part of the flange of a wide-flange beam in the structural system of a continuous beam. The results suggest that for higher flange curvature and higher width to length ratio, this effect is more prominent. Full article

Due to the coupling of the damper journal with the elastic ring and oil film, the elastic ring squeeze film damper (ERSFD) shows better dynamic performance in comparison with the traditional squeeze film damper (SFD). Therefore, a novel rigid–elastic–oil coupled mathematical model was established. The elastic ring deformation, as the key point, is solved according to the planar bending theory. Then, based on the pressure governing equation of the oil film, using the central finite difference method, the oil film pressure was addressed. Meanwhile, the Simpson method was implemented to calculate the dynamic characteristic coefficients (equivalent stiffness and damping $Ce$) of ERSFD (DCCEs). Also, we analyzed the influence of journal eccentricity, oil film radius clearance, flexibility coefficient and damping hole diameter on the DCCEs, and the results were compared and verified with the existing literature. The sensitivity of each parameter to the DCCEs was analyzed by using the linear regression method. According to the results, the flexibility coefficient has the greatest effect on the DCCEs, followed by the oil film radius clearance. The eccentricity of the journal and damping hole diameter have the least impact. This work will provide a theoretical basis for reflecting on the bearing dynamic characteristics more truly and accurately. Full article

Toppling-sliding failure is a typical mode of deep-seated toppling failure. In this mode, massive collapsed rock masses form the main sliding body, which is sensitive to rainfall events and prone to instability under rainfall due to its unique slope structure. In the present study, based on the detailed investigation on the geology and deformation characteristics, we studied the deformation and failure mechanism of a large-scale deep-seated toppling in Nandongzi Village, Pingquan City, Hebei Province. We constructed an engineering geology model to describe the toppling-sliding failure under rainfall. In addition, based on the saturated–unsaturated seepage theory and using the SLOPE/W and SEEP/W modules in the GeoStudio software, we explored the seepage law and factors controlling the seepage failure of toppling-sliding under rainfall. From surface to interior, the slope can be divided into topplingalling zone, strong toppling zone, slight toppling zone, and non-deformation zone. The geological structure consisting of an upper strong slab and an underlying weak rock layer, controls the early deformation, and the deformation and failure mode is compressing-bending-toppling. Due to the influence of excavation and rainfall, the sliding movements occur along planar rupture planes in the toppling-falling zone in the later stage, during which the failure mode switches to creeping-cracking. At present, the stability of the slope is highly sensitive to rainfall. When the rainfall intensity exceeds 220 mm/day (50 years return period storm), the factor of safety will fall below 1.05 and subsequently the sliding failure may be triggered. Because of the difference in permeability characteristics between the toppling-falling zone and the strong toppling zone, high pore-water pressure is developed at their boundary, leading to a drastic decrease in the factor of safety. Specifically, the more considerable difference in permeability, the lower the safety factor. Overall, this study is significant in scientific guiding for evaluating and preventing such slope failures. Full article

A category of metamaterials consisting of chiral cytosolic elements assembled periodically, in which the introduction of a rotatable annular structure gives metamaterials the ability to deform in compression–shear, has been a focus of research in recent years. In this paper, a compression–shear coupling model is developed to predict the compressive deformation behaviour of chiral metamaterials. This behaviour will be analysed by coupling the rotation of the annular node and the bending characteristics of ligament beam, which are obtained as a function of the length of ligament beam and the angle of rotation at the end of the beam. The shape function of the ligament beam under large deformation is obtained based on the elliptic integral theory; the function characterises the potential relationship between key parameters such as displacement and rotation angle at any point on the ligament beam. By simulating the deformation of cells under uniaxial compression, the reasonableness of the large deformation model of the ligament beam is verified. On this basis, a chiral cell-compression mechanical model considering the ductile deformation of the annular node is established. The compression–shear deformation of two-dimensional planar chiral metamaterials and three-dimensional cylindrical-shell chiral metamaterials was predicted; the offset displacements and torsion angles agreed with the experimental and finite element simulation results with an error of less than 10%. The developed compression–shear coupling model provides a theoretical basis for the design of chiral metamaterials, which meet the need for the precise control of shapes and properties. Full article

A three-dimensional auxetic structure based on a known planar configuration including a design parameter producing asymmetry is proposed in this study. The auxetic cell is designed by topology analysis using classical Timoshenko beam theory in order to obtain the required orthotropic elastic properties. Samples of the structure are fabricated using the ABSplus fused filament technique and subsequently tested under quasi-static compression to statistically determine the Poisson’s ratio and Young’s modulus. The experimental results show good agreement with the topological analysis and reveal that the proposed structure can adequately provide different elastic properties in its three orthogonal directions. In addition, three point bending tests were carried out to determine the mechanical behavior of this cellular structure. The results show that this auxetic cell influences the macrostructure to exhibit different stiffness behavior in three working directions. Full article

This paper represents a multidisciplinary approach to biomechanics (medicine engineering and mathematics) in the field of collum femoris fractures, i.e., of osteosyntheses with femoral/cancellous screws with full or cannulated cross-sections. It presents our new numerical model of femoral screws together with their stochastic (probabilistic, statistical) assessment. In the first part of this article, the new simple numerical model is presented. The model, based on the theory of planar (2D) beams on an elastic foundation and on 2nd-order theory, is characterized by rapid solution. Bending and compression loadings were used for derivation of a set of three 4th-order differential equations. Two examples (i.e., a stainless-steel cannulated femoral screw and full cross-section made of Ti6Al4V material) are presented, explained, and evaluated. In the screws, the internal shearing forces, internal normal forces, internal bending moments, displacement (deflections), slopes, and mechanical stresses are calculated using deterministic and stochastic approaches. For the stochastic approach and a “fully” probabilistic reliability assessment (which is a current trend in science), the simulation-based reliability assessment method, namely, the application of the direct Monte Carlo Method, using Anthill software, is applied. The probabilities of plastic deformations in femoral screws are calculated. Future developments, which could be associated with different configurations of cancellous screws, nonlinearities, experiments, and applications, are also proposed. Full article

A model for the low-frequency magnetoelectric (ME) effect that takes into consideration the bending deformation in a ferromagnetic and ferroelectric bilayer is presented. Past models, in general, ignored the influence of bending deformation. Based on the solution of the equations of the elastic theory and electrostatics, expressions for the ME voltage coefficients (MEVCs) and ME sensitivity coefficients (MESCs) in terms of the physical parameters of the materials and the geometric characteristic of the structure were obtained. Contributions from both bending and planar deformations were considered. The theory was applied to composites of PZT and Ni with negative magnetostriction, and Permendur, or Metglas, both with positive magnetostriction. Estimates of MEVCs and MESCs indicate that the contribution from bending deformation is significant but smaller than the contribution from planar deformations, leading to a reduction in the net ME coefficients in all the three bilayer systems. Full article

This paper focuses on the effects of transverse shear and root rotations in both symmetric and asymmetrical end-notched flexure (AENF) interlaminar fracture toughness tests. A theoretical model is developed, whereas the test specimen is subdivided into four regions joined by a rigid interface. The differential equations for the deflection and rotations of each region are solved within both the Euler–Bernoulli simple beam theory (SBT) and the more refined Timoshenko beam theory (TBT). A concise analytical equation is derived for the AENF deflection profile, compliance, and transverse shearing forces as a function of the specimen geometry, stacking sequence, delamination length, and fixture span. Modeling results are compared with numerical finite element analyses, obtaining a very good agreement. Performed analyses suggest that even in the case of symmetrical and unidirectional laminates considered as pure mode II fracture, a complex compression/tension and bending moment state is present, as well as a slight contribution of anti-planar shear at the vicinity of the crack tip. Full article

This paper presents a theory for the analytical determination of internal forces in the links of planar linkage mechanisms and manipulators with statically determinate structures, considering the distributed dynamic loads. Linkage mechanisms and manipulators were divided into elements and joints. Discrete models were created for both the elements and the entire mechanism. The dynamic equations of equilibrium for the discrete model of the elements and the hinged and rigid joints, under the action of longitudinal and transverse distributed dynamic trapezoidal loads, were derived. In the dynamic equations of the equilibrium of the discrete model of the elements and joints, the connections between the components of the force vector in the calculated cross-sections and the geometric, physical, and kinematic characteristics of the element were established for its plane-parallel motion. According to the developed technique, programs were created in the Maple system, and animations of the motion of the mechanisms were produced. The links were constructed with the intensity of transverse- and longitudinal-distributed dynamic loads, bending moments, and shearing and normal forces, depending on the kinematic characteristics of the links. Full article