Bellows compensators are critical components in pipeline systems, designed to absorb thermal expansions, vibrations, and pressure reflections. Ensuring their operational reliability requires accurate prediction of the stress–strain state (SSS) and stability under internal pressure. This study presents a comprehensive mathematical model for analyzing corrugated bellows compensators, formulated as a boundary value problem for a system of partial differential equations (PDEs) within the Kirchhoff–Love shell theory framework. Two numerical approaches are developed and compared: a finite difference method (FDM) applied to a reduced axisymmetric formulation to ordinary differential equations (ODEs) and a finite element method (FEM) for the full variational formulation. The FDM scheme utilizes a second-order implicit symmetric approximation, ensuring stability and efficiency for axisymmetric geometries. The FEM model, implemented in Ansys 2020 R2, provides high fidelity for complex geometries and boundary conditions. Convergence analysis confirms second-order spatial accuracy for both methods. Numerical experiments determine critical pressures based on the von Mises yield criterion and linearized buckling analysis, revealing the influence of geometric parameters (wall thickness, number of convolutions) on failure mechanisms. The results demonstrate that local buckling can occur at lower pressures than that of global buckling for thin-walled bellows with multiple convolutions, which is critical for structural reliability assessment. The proposed combined approach (FDM for rapid preliminary design and FEM for final verification) offers a robust and efficient methodology for bellows design, enhancing reliability and reducing development time. The work highlights the importance of integrating rigorous PDE-based modeling with modern numerical techniques for solving complex engineering problems with a focus on structural integrity and long-term performance.

Traditional bone plates provide reliable fracture fixation; however, their high stiffness can cause stress shielding, thereby reducing mechanical stimulation of the bone tissue and slowing its regeneration. The biomechanical performance of a titanium plate with a localized porous structure for osteosynthesis of the radial shaft was investigated in this study. Three designs were considered: a solid plate and two plates with localized porous regions measuring 10 × 10 mm and 10 × 15 mm. The finite element analysis of the bone–plate system was performed using MSC Patran/Nastran, with rigid fixation of the proximal end of the bone and sequential application of an axial compressive load of 100 N, bending, and torsion with a moment of 1 N·m. Biomechanical performance was evaluated based on von Mises equivalent stress, fragment displacement (FD), interfragmentary movement (IFM), interfragmentary strain (IFS), and strain energy density (SED). To confirm the manufacturability of the design, the plate was fabricated from Ti–6Al–4V alloy using laser powder bed fusion (LPBF), and the geometry of the porous structure was verified by scanning electron microscopy. The results showed that the localized porous structure altered the load distribution between the plate and the bone, resulting in an increase in local stresses in the bone under the investigated loading conditions. These changes indicate an alteration in the mechanical environment within the bone, which may potentially affect conditions related to fracture healing. Among the investigated configurations, the plate with a 10 × 10 mm porous insert demonstrated the most balanced mechanical characteristics in terms of stresses in the implant, stress distribution in the bone, and structural stability.

Reliable and energy-efficient capacity control in high-pressure single-rotor screw compressors requires precise regulation of adjustable ring mechanisms operating under combined gas and thermal loading. Thermo-mechanical deformation, friction-induced torque demand, and stress concentration near discharge windows significantly influence structural integrity, clearance stability, and actuation performance. This study presents an integrated thermo-structural and analytical investigation of a regulating ring system with a hydraulic wedge-groove drive concept. Three groups of geometric variants (nine configurations total) were analyzed using coupled Steady-State Thermal and Static Structural finite element modeling in ANSYS 19.2. Thermal asymmetry between suction (22 °C) and discharge (120 °C) regions produced peak thermally induced deformation of 0.17–0.18 mm, consuming up to 60–70% of nominal operating clearance. Neglecting thermal effects underestimated peak thermally induced structural deformation of the regulating ring by 12–15%. Among the configurations, variant 2b provided the most balanced response, reducing peak equivalent stress by 12–15% and required actuation torque by 8–11%. An analytical model for friction torque and driving force was derived based on distributed contact pressure. The results reveal quadratic sensitivity of torque to contact radius and strong dependence on groove geometry. The proposed framework supports reliable clearance design and efficient actuation in heavy-duty rotating machinery.

The hydrodynamic and tribological characteristics of a sucker-rod pump valve assembly with a modified seat equipped with a turbulizer are investigated. The study aims to extend service life by controlling the flow structure and reducing contact loads in the ball–seat pair. A combined approach is employed, integrating computational fluid dynamics (CFD) simulations with physical experiments. The results show that an increase in turbulence intensity does not lead to a proportional improvement in performance due to energy dissipation; however, an optimal turbulizer geometry is identified that ensures directed swirl flow and efficient transfer of angular momentum. It is established that the theoretical number of ball rotations in oil is 24 over 5 s, whereas the experiment conducted in water yields 30 rotations over the same period, which is attributed to viscosity effects. An empirical relationship is proposed to describe transitions between the “free flow,” “flow with ball,” and “turbulized flow” regimes, taking into account the rheological properties of the fluid; the validity of the model is confirmed by computational experiments. It is demonstrated that reducing contact forces is a more critical factor than maximizing hydraulic efficiency.

Мақала білек сүйегінің дистальды бөлігінің сынықтарын емдеуде қолданылатын остеосинтездік пластиналардың құрылымын инженерлік және технологиялық талдауға негізделген. Зерттеудің мәселесі әдеттегі титаннан жасалған импланттардың сүйек тінімен жанасудағы биомеханикалық сәйкессіздіктің негізінде туындады. Mimics, PATRAN/ MARC, соңғы элемент әдісі СЭӘ осы аталған бағдарламаларда модельдеу мен кернеулі-деформацияланған күйді соңғы элементтер әдісінде талдау жүргізілді. Зерттеу кезінде сүйек құрылымының 3D моделі 60-80 жас аралығындағы пациенттердің КТ деректері Mimics бағдарламасында өңделді. Антропометриялық өлшеулер негізінде 11 градус иіні мен бекіту тесігі 5 градус бұрышпен оңтайландырылған пластинаның құрылымы дайындалды. NASTRAN/PATRAN бағдарламасы мен СЭӘ әдісімен есептеулер жүргізіліп пластикалығы жоғары ВТ1-0 таза техникалық титанының иілуі мен бұралуы кезіндегі төзімділігі анықталды. Лазерлік және электр эрозияық кесу әдістерін салыстыру кезінде лазерлік өңдеу бет сапасының жоғарырақ көрсеткіштерін көрсетті. Осы себепті волярлық пластиналарды дайындауда аталған технологияны қолдану тиімді деп санаймыз. Зерттеулердің нәтижелеріне қарай биоүйлесімді пластиналы импланттарды дайындауда ВТ1-0 таза техникалық титанының ерекшелігін дәлелдейді. Пластинаның ерекше биоүйлесімділігі, коррозияға төзімділігі мен икемділігінің төмендігі остеосинтез пластиналарын өндіру үшін дұрыс шешім екені анықталды. Сонымен қатар медицинада кеңінен қолданылатын легирленген титан қорытпасымен салыстырғанда білек сүйегінің серпімділігіне сәйкес келетіндігі, уытты бөлмейтіндігі ерекше орын алды. Кілтті сөздер: имплантат, остеосинтез, кернеулі-деформацияланған күй, ВТ1-0 техникалық титан, биомеханика, сүйек тіндері, пластина.

The application of carbon fiber-reinforced polyetheretherketone (CFR-PEEK) composites in osteosynthesis implants represents a promising approach to mitigating the stress-shielding effect associated with the high stiffness of conventional metallic implants. This study aimed to experimentally and numerically evaluate the effects of short carbon fiber content and the orthotropic mechanical properties of CFR-PEEK on the structural strength of osteosynthesis plates and load distribution within the bone–plate system. The investigation employed a multiscale approach integrating micromechanical modeling using the Mori–Tanaka homogenization method in Digimat-MF, experimental mechanical testing of FDM-fabricated CFR-PEEK specimens containing 10 wt.% carbon fibers, and finite element analysis of osteosynthesis plates made of CFR-PEEK with 10 and 30 wt.% carbon fibers and Ti-6Al-4V using MSC Patran/Marc. CFR-PEEK 30% specimens were neither fabricated nor experimentally tested. Their mechanical properties were predicted using Digimat-MF by applying correction factors derived from experimental data obtained for CFR-PEEK 10%. The results demonstrated that increasing the carbon fiber content from 10 to 30 wt.% enhanced the longitudinal elastic modulus. Experimental testing of CFR-PEEK containing 10 wt.% carbon fibers revealed an elastic modulus ranging from 1.76 to 3.10 GPa and a tensile strength of 47–54 MPa. Following process-related adjustments to the material properties, finite element simulations of the bone–plate system were performed under an axial load of 50 N. The calculated load shielding indices were 94.3% for Ti-6Al-4V, 28.6% for CFR-PEEK 10%, and 54.3% for CFR-PEEK 30%, indicating the potential of composite implants to improve mechanical load transfer to the surrounding bone tissue. A preliminary strength assessment based on the three-dimensional Tsai–Hill failure criterion yielded failure indices of 15.577 and 1.112 for CFR-PEEK 10% and CFR-PEEK 30%, respectively, under the assumed material strength parameters. Critical stress concentrations were predominantly localized around the fixation holes. These findings highlight the trade-off between reducing stress shielding and ensuring the structural integrity of composite osteosynthesis plates. The results further emphasize the need for localized optimization of fixation regions to improve mechanical reliability without increasing the overall implant thickness.