Simulation of Thermoelastic Behaviour of Spacecraft Structures

The objective of every scientific and Earth observation mission is to do observations of various physical effects in space or on planet surfaces. Also missions to the Sun aim at measuring different physical phenomena. All these observations have in common that these want to measure the distribution of different properties over a planet surface or the sky to capture space as deep possible. Advances in the optical sensors and radar technologies offer the potential to do these observations with increasing resolution allowing to enhance the quality of the information collected from space.

Thermoelastic aspects in the development of spacecraft are illustrated with a few examples.

In this chapter, the main physical parameters involved in thermoelastic effects, the coefficient of thermal expansion (CTE) and Young’s modulus, are discussed. The equilibrium and constitutive relations between stress and strain including thermoelastic effects are briefly recapitulated. At the end of the chapter, a summary of governing equilibrium and constitutive equations is given.

The physics of thermoelastic involves both thermal and structural phenomena that require to be handled together. Consequently, thermoelastic analysis has to be considered as an integral process including both related disciplines with close interaction of the models. This interaction imposes an important and often overlooked constraint: Making decisions about the importance of a temperature field with only the knowledge of a temperature field is in general not possible and always requires the computation of the structural thermoelastic response.

A spacecraft is going through different phases of a mission. Each of these phases has its own characteristics in terms of thermal environment. The objectives of these different phases drive the difference in focus of thermoelastic analyses from one phase to the other. The lumped parameter thermal analysis method typically used for spacecraft thermal analysis is summarised. Transient thermal analysis is a common analysis approach for simulating time-varying thermal environments along the orbit around a planet. Special attention is paid to the difference between thermal analysis for thermal control and thermal analysis for thermoelastic.

The thermal stresses and thermal deformations are the responses of a structure due to temperature fields as one of the applied loads. These responses of a structure are computed through thermoelastic analyses. As for many structural problems, also for simulating the thermoelastic response of a structure, the finite element (FE) method is the method mostly used. Using the fundamentals of the FE method and implementations in the finite elements, this chapter discusses the different finite element types and their adequacy to simulate thermoelastic responses. Within a space project, several types of structural analysis, in general all based on the FE method, are run. For practical reasons, there is a preference to use the same model for all these analyses. The single model that is commonly used is the dynamic model, developed for simulating the structural dynamics, which is as well an important design driving aspect for a spacecraft. However, a model, adequate to simulate the dynamic responses of a structure, may not always be able to represent properly the thermoelastic behaviour. Some limitations of typical dynamic models are explained, and suggestions are provided to adapt or refurbish the dynamic model to enhance the quality of the computed thermoelastic responses.

In general, the thermal model has a lower resolution than the structural FE model used for linear thermoelastic analysis. Besides a difference in mesh resolution, the methods used for the thermal and structural analyses differ as well. This complicates the transfer, also referred to as temperature mapping, of the calculated temperatures of the thermal model as temperature loading on the FE model for thermoelastic response calculation. This chapter discusses four different systematic methods for temperature mapping.

The system equations of the prescribed average temperature (PAT) mapping method are explained. The method allows to transfer the temperature field as computed with the lumped parameter thermal analysis to the finite element model while respecting the assumptions of the lumped parameter method.

The generation of linear conductors for a thermal lumped parameter model is in many cases a time-consuming task. The finite element method can help to automate this process and in addition increase the quality of these conductors especially for complex-shaped parts. Three methods for the generation of linear conductors between pairs of the thermal nodes are discussed first. One of these three is the “Far Field” method implemented in ESATAN-TMS. The other two methods are based on static reduction of the finite element conduction matrix and a steady-state solution technique, respectively. The PAT method provides relations between thermal nodes and finite element nodes consistent with the lumped parameter assumption. The system equation used for the temperature mapping with the PAT method is exploited to determine a complete conductive network between in principle all conductively connected nodes in the thermal model.

Instead of a single model for one discipline, thermoelastic analysis involves at least a thermal model and a structural model. In many cases, these two analysis steps are followed by a RF or optical simulation to determine the impact on the performance of the instrument of the thermoelastic responses. Each analysis step is accompanied with uncertainties. Besides the thermal and structural analyses, the transfer of temperature data introduces additional uncertainties. A method based on factors of safety, as is used in structural analysis to cover uncertainties, is discussed. Although the method can be pragmatic, this approach is often lacking a physical basis, may not be compatible with the requirements for specific cases, and the values used for these factors are to a large extent ambiguous. Stochastic approaches are known to be powerful for estimating ranges in the responses due to variation of parameters. Although the Monte Carlo method is well known and robust, it is computationally expensive. Promising alternative methods to quantify uncertainties of the responses, among many others, are the Latin hypercube sampling (LHS) method and the Rosenblueth \(2k+1\) Point Estimates Moments (PEM) method. The significance of the random design variables on the random output is detected through a sensitivity analysis, i.e. by a regression analysis method or as an intermediate result of the Rosenblueth PEM method. The section concludes with several worked out examples.