Рассмотрен стержень постоянного сечения и конечной длиной, по торцам которого происходит теплообмен с окружающей средой, а сбоку которого подается тепловой поток. Получено аналитическое решение задачи определения термомеханических характеристик стержня: закон распределения температуры и перемещения, удлинение, осевое термическое усилие, термо-упругие, температурные, упругие напряжения и деформации стержня. Получено графическое представление этих характеристик.

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.