Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived ...Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.展开更多
To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spheri...To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.展开更多
以某B型不锈钢地铁车体为对象,研究建模方法对车体有限元分析的影响,包括静强度、刚度和模态分析。首先采用CAD建模软件建立了车体的精细几何模型,然后基于厚度叠加原理,建立了无点焊等效厚度的车体板壳模型,同时建立了采用CWELD焊点单...以某B型不锈钢地铁车体为对象,研究建模方法对车体有限元分析的影响,包括静强度、刚度和模态分析。首先采用CAD建模软件建立了车体的精细几何模型,然后基于厚度叠加原理,建立了无点焊等效厚度的车体板壳模型,同时建立了采用CWELD焊点单元精确模拟点焊的车体板壳模型。在此基础上,依据BS EN 12663-1:2010标准,确定了车体强度评价载荷工况,对比分析了两种建模方法的有限元分析结果,验证了简化建模方法的有效性。对两种模型车体理行计算,模态分析结果表明,有点焊模型模态频率较高,刚度结果表明有点焊模型刚度较大,静强度结果表明有点焊模型强度较高。采用等厚度叠加原理的车体建模计算结果偏于保守,在工程设计和分析中采用是可行的。展开更多
文摘Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.
文摘To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.
文摘以某B型不锈钢地铁车体为对象,研究建模方法对车体有限元分析的影响,包括静强度、刚度和模态分析。首先采用CAD建模软件建立了车体的精细几何模型,然后基于厚度叠加原理,建立了无点焊等效厚度的车体板壳模型,同时建立了采用CWELD焊点单元精确模拟点焊的车体板壳模型。在此基础上,依据BS EN 12663-1:2010标准,确定了车体强度评价载荷工况,对比分析了两种建模方法的有限元分析结果,验证了简化建模方法的有效性。对两种模型车体理行计算,模态分析结果表明,有点焊模型模态频率较高,刚度结果表明有点焊模型刚度较大,静强度结果表明有点焊模型强度较高。采用等厚度叠加原理的车体建模计算结果偏于保守,在工程设计和分析中采用是可行的。
