Mathematics and Mechanics of Solids最新文献_第4页

Stability analysis of thin cylindrical shells under pure and three-point bending 薄圆柱壳在纯弯曲和三点弯曲下的稳定性分析

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241259134

Péter Máté, András Szekrényes

{"title":"Stability analysis of thin cylindrical shells under pure and three-point bending","authors":"Péter Máté, András Szekrényes","doi":"10.1177/10812865241259134","DOIUrl":"https://doi.org/10.1177/10812865241259134","url":null,"abstract":"Cylindrical shells curved in only one direction show an interesting behaviour when bent, especially if they remain completely in the elastic region and do not undergo plastic forming. This can be observed in their most common application: the measuring tape. They can be coiled easily because of the loss of stability of their cross-sections, which makes transportation of long shells efficient. This property could be very useful if one could use such a one-way curved shell as a beam, which could be transported and deployed easily. The aim of this study is to observe the behaviour of such a shell, under pure bending load, with special emphasis on the stability loss of the cross-section. In this paper, analytical, semi-analytical, and finite-element methods are used for the description of the shell. The solution derived here uses a variable cross-section Euler–Bernoulli beam model combined with elements of the Kirchhoff plate theory without the shallow shell assumption. It is assumed that the cross-section remains circular and does not change its length. For a universal description, dimensionless parameters and variables are introduced. The semi-analytical investigation revealed that the snap-through ability of the shell may not exist for certain cross-sections which can be presented on a stability map. The derived model reveals the existence of a limiting point between the cross-section deformation modes for larger cross-section angles. In the article, ready-to-use analytical and semi-analytical solutions are given for the critical load and stability map of these shells, which are compared to similar shallow shell models from the literature and the finite-element solution of the problem. The finite-element method also revealed that for a dimensionless description, a length-cross-section radius parameter should be introduced to describe the three-point bending scenario.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Predicting and explaining nonlinear material response using deep physically guided neural networks with internal variables 利用带内部变量的深度物理引导神经网络预测和解释非线性材料响应

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241257850

Jacobo Ayensa-Jiménez, Javier Orera-Echeverría, Manuel Doblare

{"title":"Predicting and explaining nonlinear material response using deep physically guided neural networks with internal variables","authors":"Jacobo Ayensa-Jiménez, Javier Orera-Echeverría, Manuel Doblare","doi":"10.1177/10812865241257850","DOIUrl":"https://doi.org/10.1177/10812865241257850","url":null,"abstract":"Nonlinear materials are often difficult to model with classical state model theory because they have a complex and sometimes inaccurate physical and mathematical description, or we simply do not know how to describe such materials in terms of relations between external and internal variables. In many disciplines, neural network methods have emerged as powerful tools to identify very complex and nonlinear correlations. In this work, we use the very recently developed concept of physically guided neural networks with internal variables (PGNNIVs) to discover constitutive laws using a model-free approach and training solely with measured force–displacement data. PGNNIVs make a particular use of the physics of the problem to enforce constraints on specific hidden layers and are able to make predictions without internal variable data. We demonstrate that PGNNIVs are capable of predicting both internal and external variables under unseen loading scenarios, regardless of the nature of the material considered (linear, with hardening or softening behavior and hyperelastic), unravelling the constitutive law of the material hence explaining its nature altogether, endowing the method with some explanatory character that distances it from the traditional black box approach.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"69 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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In recognition of the 80th birthday of Ray Ogden 纪念雷-奥格登 80 岁生日

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-25 DOI: 10.1177/10812865241257268

Luis Dorfmann, José Merodio, Raimondo Penta, Prashant Saxena

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A partially debonded rigid elliptical inclusion with a liquid slit inclusion occupying the debonded portion 部分脱粘的刚性椭圆形包合物，脱粘部分含有液体狭缝包合物

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-06-22 DOI: 10.1177/10812865241257534

Xu Wang, Peter Schiavone

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Critical velocities of a three-layer composite tube incorporating the rotary inertia and material anisotropy 包含旋转惯性和材料各向异性的三层复合管的临界速度

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-06-21 DOI: 10.1177/10812865241250015

Xin-Lin Gao

{"title":"Critical velocities of a three-layer composite tube incorporating the rotary inertia and material anisotropy","authors":"Xin-Lin Gao","doi":"10.1177/10812865241250015","DOIUrl":"https://doi.org/10.1177/10812865241250015","url":null,"abstract":"Critical velocities of a three-layer composite tube subjected to a uniform internal pressure moving at a constant velocity are obtained in closed-form expressions. A Love–Kirchhoff thin shell model including the rotary inertia and material anisotropy effects is used in the formulation. The composite tube is made of three perfectly bonded cylindrical layers of dissimilar materials, each of which can be orthotropic, transversely isotropic, cubic or isotropic. Closed-form formulas for the critical velocities are first derived for the general case by incorporating the effects of material anisotropy, rotary inertia and radial stress. Specific formulas are then obtained for composite tubes without the rotary inertia effect and/or the radial stress effect and with various types of material symmetry for each layer as special cases. It is also shown that the current model for three-layer tubes can be reduced to those for single- and two-layer tubes. To illustrate the newly derived formulas, an example is provided for a composite tube consisting of an isotropic inner layer, an orthotropic core, and an isotropic outer layer. All four critical velocities of the composite tube are computed using the new closed-form formulas. Three values of the lowest critical velocity of the three-layer composite tube are analytically obtained from three sets of the new formulas, which agree well with the value computationally determined by others.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"24 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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Some qualitative results in hyperbolic two-temperature generalized thermoelasticity 双曲双温广义热弹性中的一些定性结果

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-06-02 DOI: 10.1177/10812865241253208

Rashmi Prasad, Roushan Kumar

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Topology optimization of continuous fiber-reinforced composites using Shepard interpolation and its design variable reduction 利用谢泼德插值及其设计变量减少法优化连续纤维增强复合材料的拓扑结构

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-06-01 DOI: 10.1177/10812865241253520

Xinze Guo, Kemin Zhou

{"title":"Topology optimization of continuous fiber-reinforced composites using Shepard interpolation and its design variable reduction","authors":"Xinze Guo, Kemin Zhou","doi":"10.1177/10812865241253520","DOIUrl":"https://doi.org/10.1177/10812865241253520","url":null,"abstract":"In the design optimization of fiber-reinforced composites, spatial material discontinuity is considered intractable within the manufacturing reality imposed by advanced technologies. This paper presents a topological optimization framework based on truss-like material to design composite structures with continuous fiber. Specifically, the fiber morphology at the scattered design points, which controls the orientation and volume fraction, is taken as design variables. Using the Shepard interpolant scheme, the fiber morphology at any given computational point is interpolated by scattered design variables within a certain circular influence domain. The employed interpolation inherently ensures the spatial continuity and range-restricted of the physical field in an element-independent manner. Since separating the design variable field and analysis mesh on two independent sets of points, this method is well suited for using a sparse design variable field. The computational savings are compelling due to the reduced number of design variables without significantly restricting the design freedom. Numerical instability such as checkerboard and mesh dependencies vanished as no intermediate densities are suppressed in optimization. The continuous fiber-reinforced composites (CFRCs) in the form of truss-like continua are ready to be manufactured with the aid of a simple post-processing. Several numerical examples are investigated to demonstrate the feasibility and effectiveness of the proposed formulation and numerical techniques.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"42 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Special issue: “Integrated approaches for the mechanics of masonry structures: Novel strategies for experimental characterization, mathematical modelling and computer simulations” 特刊："砌体结构力学的综合方法：实验表征、数学建模和计算机模拟的新策略"

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-05-30 DOI: 10.1177/10812865241256800

Roberto Fedele, Gabriele Milani, Francesco dell’Isola

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Thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load 热效应对承受动态反面载荷的压磁半空间瞬态行为的影响

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-05-27 DOI: 10.1177/10812865241251470

Xiang Zhou, Guoshuang Shui

{"title":"Thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load","authors":"Xiang Zhou, Guoshuang Shui","doi":"10.1177/10812865241251470","DOIUrl":"https://doi.org/10.1177/10812865241251470","url":null,"abstract":"Considering the importance of understanding the propagation of transient waves in the piezomagnetic solids, the thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load is investigated analytically in this paper. Using one-sided, two-sided Laplace transformation and Cagniard–de Hoop (CH) technique, an efficient and accurate analytical derivation for the solution of the anti-plane displacement, shear stress, magnetic potential, and induction in Laplace domain is presented. The study shows that the thermal stresses developed in x-axis and y-axis directions have significant influence on the transient response of the half-space. The magnetic induction [Formula: see text] increases obviously when the thermal stress is applied in x-axis direction, while it decreases when the thermal stress is applied in y-axis direction. Approaching time of magnetic induction [Formula: see text] and [Formula: see text] will become longer with higher thermal stress in x-axis direction. With the growth of the thermal stress in x-direction, contribution from the electromagnetic–elastic head (EH) wave increases, while the contribution from the shear elastic (SE) wave and the static value of shear stress decrease.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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Homogenization of nonlinear Cosserat plate including growth theory when the thickness of the plate and the size of the in-plane heterogeneities are of the same order of magnitude 当板厚度和面内异质大小处于同一数量级时，包括生长理论在内的非线性 Cosserat 板的均质化问题

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-05-13 DOI: 10.1177/10812865241243086

Erick Pruchnicki

{"title":"Homogenization of nonlinear Cosserat plate including growth theory when the thickness of the plate and the size of the in-plane heterogeneities are of the same order of magnitude","authors":"Erick Pruchnicki","doi":"10.1177/10812865241243086","DOIUrl":"https://doi.org/10.1177/10812865241243086","url":null,"abstract":"In this work, we present a new two-scale finite-strain plate theory for highly heterogeneous plates described by a repetitive periodic microstructure. Two scales exist, the macroscopic scale is linked to the entire plate and the microscopic one is linked to the size of the heterogeneity. This work aims to propose such a theory for thick plates in a nonlinear setting when the thickness and the size of heterogeneities are of the same order of magnitude. The homogenization theory for large deformation with growth is suitable for the modelization of nearly incompressible plant tissue. This model is suitable for wavy leaves. For thick plates, the transverse normal stress and transverse shearing are modelized at both microscopic and macroscopic levels. At the macroscopic level, we consider a nonlinear Cosserat plate model. At the microscopic level, we impose that the average of contribution of the microscopic displacement to rotation angles is equal to zero. We also deal with the problem of boundary layer problem near the lateral boundary. The model recently proposed by Pruchnicki is valid for thin heterogeneous plates; we present an extension for thick plates that takes into account both transverse normal stress and shearing. This model is equivalent to the first model presented but it involves a second-order derivative of the macroscopic displacement field.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"68 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0