Thermally induced stresses in cross-ply composite tubes

This chapter introduces the calculus of variations and associated mathematical operators on functionals, which are used to formulate boundary value problems in structural mechanics. Weak forms of equilibrium are derived in terms of the principle of virtual work and the theorem of minimum potential energy. These are used to establish the governing field equations (Euler–Lagrange differential equations) and associated geometric, natural, or mixed boundary conditions. Weak forms of kinematic compatibility are derived in terms of the principle of complementary virtual Work and the theorem of minimum complementary potential energy. Examples are provided for each.

Time-dependent stress variations in symmetrically viscoelastic composite laminates under uniaxial tensile load

A comprehensive analysis of delamination and thermoelectric performance of thermoelectric pn-junctions with temperature-dependent material properties

ABSTRACTHigh specific strength and stiffness are characteristics desired for aircraft and launch vehicle domains to enhance the payload gain and performance. The mechanical properties of the composites can be further tailored by embedding structural components, such as shape memory alloys, into the passive composite structure. The present study is primarily focused on the nonlinear free vibration analysis of spherical and cylindrical composite shell panels embedded with shape memory alloy fibers. The nonlinear finite element governing equations based on the higher-order shear deformation plate theory and principle of virtual work with nonlinear von-Karman strain displacement relations are employed for the analysis. The temperature-dependent material properties of shape memory alloy are considered in the formulation. A nine-noded isoperimetric element is accounted for synthesizing the element for the finite formulation. The Young's modulus and the recovery stress vary with temperature and higher nonlinearity. The incremental method is used to generate the inputs for the temperature-dependent nonlinear properties of materials. The temperature change is divided by many small temperature increments. The temperature-dependent material properties are assumed constant during the small increment. The mechanics of shape memory alloy in substrate are presented and the governing equation of laminated composite with shape memory alloy is obtained and implemented in the MATLAB 7.8 program.

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Non-linear thermal response of sandwich panels with a flexible core and temperature dependent mechanical properties

A new nonlinear finite element formulation is presented to predict the thermal buckling and flutter boundaries of shape memory alloy hybrid composite cylindrical panels at elevated temperatures. The governing equations are obtained using Marguerre curved-plate theory and the principle of virtual work. The effect of large deflection is included in the formulation through the von Karman nonlinear strain-displacement relations. To account for the temperature dependence of material properties, the thermal strain is stated as an integral quantity of the thermal expansion coefficient with respect to temperature. The aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The Newton―Raphson iteration method is employed to obtain the nonlinear thermal postbuckling deflections, and a frequency-domain solution is presented to predict the critical dynamic pressure at elevated temperatures. Numerical results are presented to illustrate the effect of shape memory alloy fiber embeddings, temperature rise, height-to-thickness ratios, and boundary conditions on the panel response.

Three-dimensional thermal buckling analysis of functionally graded material structures using a modified FSDT-based solid-shell element

This article investigates the nonlinear stability of eccentrically stiffened moderately thick plates made of functionally graded materials (FGM) subjected to in-plane compressive, thermo-mechanical loads. The equilibrium and compatibility equations for the moderately thick plates are derived by using the first-order shear deformation theory of plates, taking into account both the geometrical nonlinearity in the von Karman sense and initial geometrical imperfections, temperature-dependent properties with Pasternak type elastic foundations. By applying the Galerkin method and using a stress function, the effects of material and geometrical properties, temperature-dependent material properties, elastic foundations, boundary conditions, and eccentric stiffeners on the buckling and post-buckling loading capacity of the eccentrically stiffened moderately thick FGM plates in thermal environments are analyzed and discussed.

Following the basis of the ASME codes, the major nuclear components are designed to successfully avoid the fatigue failure. However, such design is generally very conservative and it is necessary to accurately assess the fatigue life of the components for the optimal life. The assessment of fatigue damage accumulation due to the thermal transients is currently performed via online fatigue monitoring systems. The algorithms for online calculation of thermal stress are one of the main components of these systems and are often based on the Green function technique (GFT), in which machine parameters such as fluid temperatures, pressures, and flow rates are converted into metal temperature transients and thermal stresses. However, since the GFT is based upon the linear superposition principle, it cannot be directly used when the temperature-dependent material properties are considered. This paper presents a methodology to consider the temperature- dependent material properties using artificial parameter method. Two cases are presented to compare the results calculated from the proposed models with those calculated by finite element method (FEM). It is found that the temperature-dependent material properties have significant influence on the maximum peak stresses which can be accurately captured by the models proposed in this work.

Fusion-based additive manufacturing of metal is particularly challenging to simulate due to the broad range of length/time scales of multiphysics phenomena to bridge. Integrated Computational Materials Engineering (ICME) offers a promising route to accelerate the design of new materials, optimize manufacturing processes, and thus improve material properties and performance. ICME heavily relies on linking multiple modelling techniques relevant to distinct length/time scales and/or different physics. While a wide range of physics-based and predictive models exist, the efficient linking of these models remains challenging. In the context of additive manufacturing, interdependent phenomena across scales include: multicomponent alloys with complex phase diagrams, multiple phase transformations and temperature-dependent properties; complex thermal exchanges in the vicinity of the melt pool; and the development of nonequilibrium grain microstructures within this melt pool. A multiscale modeling strategy (i.e. micro and macro) has been developed to simulate powder-bed fusion of metallic alloys, which combines: (1) Temperaturedependent alloy properties and phase diagrams calculated by CalPhaD, (2) macroscale thermal and thermo-mechanical simulations of the material addition and fusion using finite elements (FE), (3) Phase-field (PF) simulations of the melt pool’s solidification at the microscopic scale, and (4) Simulations of the microscopic solidification of the melt pool using cellular automaton (CA). Realistic processing parameters are used in the methodology to simulate selective laser melting (SLM) of an Inconel 718 alloy. In the first step, three-dimensional thermal and thermo-mechanical frameworks were developed – using an in-house finite element code (IRIS) and a material library (MUESLI) implemented in C++ programming language – by considering these four factors: (1) Representing the thermal input from the scanning laser, (2) A material model to specify the temperature-dependent material property in the cyclic heating and cooling environment, (3) A physics-based method to explain the layer build-up process, and (4) A laser material interaction model to account for transient thermo-mechanical phenomena. Then, the thermal model was coupled with CalPhaD and PF methods to predict the formation of microstructures at the scale of the entire melt pool. In this part, the effect of temperature-dependent properties and the necessity of taking into account differences in properties between the powder bed and the dense material have been discussed. We perform an appropriately-converged PF solidification simulation at the scale of the entire melt pool using a two-dimensional longitudinal slice of the thermal field calculated through FE simulations. This calculation has over one billion grid points, yet is performed on a single cluster node with eight graphics processing units (GPUs). These microscale simulations, with a level of detail down to individual dendrites, offer new insight into the selection of grain texture via polycrystalline growth competition under realistic SLM conditions. Finally, comparisons between phase-field (PF) and cellular automaton (CA) simulations of polycrystalline growth in a two-dimensional melt pool under additive manufacturing (powder-bed fusion) relevant conditions have been performed. The generated grain structures from local (point-by-point) measurements and grain orientation distributions that were averaged over various simulations have been compared. We investigated how the melt pool aspect ratio and the CA spatial discretization level affected the selected grain texture. Our simulations demonstrate that only PF simulations are capable of capturing the fine-grained microscopic features related to transient growth conditions and solid-liquid interface stability, such as the initial planar growth stage before its cellular/dendritic destabilization or the early elimination of unfavorably oriented grains due to neighbor grain sidebranching. CA grid refinement can only partially address the resulting disagreement between PF and CA predictions. In addition, with some variability on the CA grid and melt pool shape, overall grain distributions averaged throughout the entire melt pools of several simulations appear to lead to a noticeably better agreement between PF and CA. This research offers a helpful step in that direction by quantitatively comparing both approaches at process-relevant length and time scales, even though more effort is still needed, especially to identify the appropriate selection of CA spatial discretization and its link to characteristic microstructural length scales.

Transient responses of functionally graded double curved shallow shells with temperature-dependent material properties in thermal environment

This work presents a finite element formulation for the vibration analysis of functionally graded material (FGM) plates containing microstructural defects operating in thermal environments. The material properties are assumed to be temperature-dependent and are modeled as higher-order functions of temperature. The volume fractions of the constituent materials are varied through the plate thickness according to a power-law distribution. The effective material properties of the FGM are evaluated using both the Mori–Tanaka homogenization scheme and the rule of mixtures. The kinematics of the FGM plates are described using an efficient layerwise theory. The governing equations of motion, constitutive relations, and boundary conditions are derived using on Hamilton’s principle. The stiffness coefficients of the plates are computed using a sub-laminate mechanics approach, wherein the plate thickness is discretized into several thin sublayers, each assumed to possess uniform material properties. This approach is particularly effective for micromechanical models where exact analytical integration of stiffness coefficients is difficult due to the complex polynomial variation of properties across the thickness. A four-noded quadrilateral finite element, previously developed for laminated and FGM shells, is extended in this study to analyze the dynamic behavior of FGM plates with microstructural defects and temperature dependent material properties. The natural frequencies are obtained using a subspace iteration technique, while the transient responses under step and impulse excitations are computed using the state-space form of the governing dynamic equations. The proposed finite element model is validated against three-dimensional elasticity and Ritz-based semi-analytical solutions, demonstrating excellent accuracy and reliability across varying thermal environments. A detailed parametric study is also carried out to investigate the effects of temperature, inhomogeneity index, porosity concentration, boundary conditions, and geometric parameters on the natural frequencies and transient responses of porous FGM plates.

Multi-objective optimization of functionally graded materials with temperature-dependent material properties

Thermal postbuckling of laminated composite skew plates with temperature-dependent properties