Practical Handbook of Finite Element Method for Civil Engineers

"Solid building materials and elements such as building facade components have not only architectural-structural functions, but they are to be guards against environmental attacks on the thermal and moisture comfort of inhabited premises: if necessary, impacts should be let through; or they should be reflected or accumulated. However, the facade structural elements undergo the following impacts: solar radiation; wind load; variation of the outdoor air temperature; effects of neighbouring buildings; effects of the environmental landscape; reflection or accumulation of solar radiation followed by secondary environmental low-temperature irradiation; transfer of noxious gases and aerosols from or to the building."
Alexander Dimitrov

Introduction: The Problem of Heat and Moisture Transfer through Solid Building Elements

• Historical review of the development of the Finite elements method, presented by Darrel Pepper
• Parameters of a "Solid Wall-Environment" System
• General Field Characteristics of a Thermodynamic System
• Temperature Field
• Pressure Field
• Thermodynamic Potential of the System
• Thermodynamic Potential of the System "Solid Structural Element-Environment"
• Distribution of the Characteristics of Thermodynamic System
• Vector Characteristics of Transfer Process

A Short Survey on Theoretical Methods of Studying Heat Transfer processes in Solid Materials

• Method of Stream Surfaces
• Method of the Differential Relations
• Method of Integral forms. Design of Integral Equations
• Boundary and Initial Conditions Valid for a Solid Wall Element Formed Under the Influence of Environment
• Interaction Between air Moisture and a Vertical Facade Wall
• Wall Dehumidification (Drying)
• Wall Humidification
• Various Types of Environment-Effected Boundary and Initial Conditions for Solid Structural Elements
• Design of Boundary Conditions for Solid Structural Elements
• Boundary Conditions Under Convective Transfer Towards the Internal Wall Surface
• Boundary Conditions at the Wall External Surface
• Transfer Regarding Anisotropic Properties of Building Materials

Numerical Methods used in Engineering for the Assessment of Transfer through Solid Building Elements

• Introduction
• Use of Variational Principles in Formulating the Basic Equation of the Finite Element Method (FEM). Method of Rayleigh-Ritz
• Weighted Residuals Method (WRM)
• Introducing the Weighted Residuals Method
• Basic Stages of the Application of WRM
• Stage 1: Discretization of the Physical Space
• Stage 2: Design of Interpolation Functions
• Linear Approximating Functions (Shape Functions)
• Matrix Forms of the Approximating Functions
• Stage 3: Modeling of Transfer in a Finite Element Using a Matrix Equation (Galerkin's Method)
• Steady Transfer in One-Dimensional Finite Element
• Integral Form of the Balance of a Substance Diffusing Through One-Dimensional Finite Element
• Modified Matrix Equation for One-Dimensional Transfer
• Transfer Taking Place Through a One-Dimensional Simple Finite Element Presented in Cylindrical Coordinates
• Steady Transfer in a Two-Dimensional Finite Element
• Equation of a Two-Dimensional Simple Finite Element in Cartesian Coordinates
• Design of Transfer Equation in Cylindrical Coordinates for a Three-Noded Two-Dimensional Finite Element
• Transfer Through a Three-Dimensional Simple Finite Element-Design of the Matrix Equation of Transfer in Cartesian Coordinates
• Stage 4: Transfer in the Global Area - Design of the Matrix Equation of the Area
• Method of the Wave Front
• Method of the Global Algebraic Mathix
• Solving the System of Algebraic Equations

Four Research Topics on Transfer of Heat and Moisture through Building Elements

• Estimation of the Energy Efficiency of the Envelope Systems (Labeling of Building' Envelope)
• Choosing a Specific Energy Efficiency Metric SEM_Buil of the Labeled Buildings' Envelope System
• Choosing an Energy Benchmark of Energy Standard - ES₀
• Determination of the Energy Efficiency Class of the Building
• Correction of the Thermal Resistance Accounting for Effects of Transfer in Three-Dimensional Space
• Analysis of the Effect of Heat- and Moisture Transfer on the Physical Characteristics and the Internal Stressed State of Building Elements Operating Under Extreme Conditions
• Prediction and Avoidance of the Phase Changes of the Air Moisture Within Building Elements

Concluding Remarks
Thermo physical characteristics of building materials
Refferences

• Appendics

Application of the Integration Equations in Calculating the elements of the Matrix of the Finite Element Surface Properties and Force Vector
Application of the Derive 5 Software System in Using the FEM