Structural Engineering Services Key words:
Analysis: Linear Static, Elastic Instability, Geometric Nonlinearity, Material Nonlinearity, Contact Nonlinearity, Design Sensitivity.
Optimization: Shape, Size, Evolutionary, Multiphysics
Material models: Elastic, Elastoplastic, Viscoelastic, Hyperelastic,
Properties: Isotropic, Orthotropic and Anisotropic
Multiphysics: Aero Elasticity, Structural + Acoustics, Structural + Thermal, Piezoelectricity, FSI, Thermoelectricity
Structural Applications: Aerospace: Wing, Fuselage, Landing Gear, Rudder, Rocket Launcher
Defense: Emergency Bridges, Rocket Launcher, Bullet Proof Panels
Civil: Steel Frames, Materials Studio, Concrete Structures, Domes, Shells, Folded Plates, Façade
Industrial: Sandwich Panels, Industrial Roofing, Heavy Machinery, Heavy Duty Cranes, Storage Structures
Energy: Wind Rotor, Wind Tower, Wind Nacelle, Transmission Tower, Transmission Lines
Introduction to Structural Mechanics
Structural mechanics is a critical field of engineering that deals with the behavior of structures under various loads and conditions. Understanding how structures respond to forces, moments, and environmental factors is essential for designing safe and effective buildings, bridges, aircraft, and other engineering systems. With the advent of computational techniques, structural mechanics has evolved significantly, allowing engineers to simulate and analyze complex systems with greater accuracy and efficiency.
Use Cases in Structural Mechanics
Structural mechanics is applied across numerous domains and industries, including:
• Civil Engineering: In the design and analysis of buildings, bridges, dams, and other infrastructure, ensuring safety and stability under various loading conditions.
• Aerospace Engineering: In the design of aircraft and spacecraft components, such as wings, fuselage structures, and support frames, to withstand aerodynamic forces and thermal loads.
• Mechanical Engineering: In the analysis of machinery, automotive components, and pressure vessels, ensuring that parts can endure operational stresses and strains.
• Geotechnical Engineering: In the analysis of soil-structure interaction, ensuring that foundations and retaining walls perform adequately under loads.
Basics of Structural Mechanics
Structural mechanics is grounded in the principles of solid mechanics, focusing on the relationship between external loads and the resulting internal stresses and deformations within a material. The fundamental concepts include:
• Force: A vector quantity that causes an object to accelerate. Forces can be applied externally (e.g., wind, seismic loads) or internally (e.g., due to temperature changes).
• Stress: The internal resistance offered by a material to deformation, typically measured as force per unit area (e.g., Pascals).
• Strain: The measure of deformation representing the displacement between particles in a material body, expressed as a ratio of change in length to the original length.
• Equilibrium: The condition where the sum of forces and moments acting on a structure is zero, ensuring that the structure remains stable.
• Compatibility: The condition that deformations must be consistent across the structure, ensuring that the structure’s shape is maintained under load.
Types of Structural Analysis
Structural analysis can be broadly categorized into two types:
• Linear Static Analysis: Assumes that materials behave elastically (i.e., stress is directly proportional to strain), and the system is analyzed under static loads. This is often suitable for small deformations and simple structures.
• Nonlinear Analysis: Takes into account material and geometric nonlinearities, allowing for the analysis of large deformations, buckling, plastic behavior, and other complex interactions. This approach is necessary for structures subjected to significant loads or unusual loading conditions.
Computational Models in Structural Mechanics
Computational models play a crucial role in structural mechanics, enabling engineers to analyze complex structures using numerical methods. The most common techniques include:
• Finite Element Method (FEM): A numerical method that divides a structure into smaller, manageable elements. Each element is analyzed to understand the overall behavior of the structure under loads. FEM is widely used for its versatility and ability to handle complex geometries and material behaviors.
• Boundary Element Method (BEM): Similar to FEM, but focuses on the boundaries of the structure. BEM is particularly effective for problems involving infinite domains, such as acoustics or fluid flow around structures.
• Meshless Methods: Techniques that do not require a mesh for the computational domain, allowing for greater flexibility in modeling complex geometries and reducing computational costs.
Partial Differential Equations (PDE) in Structural Mechanics
The governing equations of structural mechanics are typically expressed as partial differential equations (PDEs), which describe the behavior of materials under various conditions. The two most common types of PDEs in structural mechanics are:
• Equations of Equilibrium: These equations represent the balance of forces and moments in the structure. For example, in linear static analysis, the equilibrium equations can be expressed as,
𝞩. 𝞼+ f = 0,
where 𝞂 is the stress tensor and f is the body force vector.
• Constitutive Equations: These equations relate stress and strain through material properties. For linear elastic materials, this relationship can be expressed as,
𝞂 =E 𝞊
where E is the Young’s modulus and 𝞊 is the strain tensor.
• Geometric Compatibility Equations: These ensure that the deformations within the material are consistent and are typically expressed as
𝞊 = (1/2) (𝞩u + (𝞩u)T)
where represents the displacement vector.
Characterizing Material Properties
Typical required material properties in structural mechanics include:
• Elastic Modulus (E): A measure of a material’s ability to deform elastically when a force is applied.
• Poisson’s Ratio (𝞶): The ratio of lateral strain to axial strain in a material under axial loading.
• Yield Strength ( 𝞂y): The stress at which a material begins to deform plastically.
• Ultimate Tensile Strength (UTS): The maximum stress a material can withstand before failure.
• Density (𝞀): A measure of mass per unit volume, critical for analyzing the weight and stability of structures.
Typical Product Performance Characteristics
The performance characteristics of structures designed using computational mechanics include:
• Load-Bearing Capacity: The ability of a structure to support applied loads without failure.
• Stability: The capacity of a structure to maintain its shape under loads without excessive deflection or collapse.
• Fatigue Resistance: The ability of a structure to withstand repeated loading cycles without failure.
• Service Life: The duration a structure can perform its intended function without significant deterioration.
• Environmental Resistance: The ability of materials to withstand environmental conditions (e.g., moisture, temperature, and chemical exposure) over time.
Summary
The field of structural mechanics within computational domains is vital for the successful design and analysis of engineering systems. With advancements in computational models, numerical methods, and innovative materials, engineers can create structures that are not only safe and efficient but also capable of meeting the challenges of modern engineering demands. By continuously evolving and integrating new technologies, the potential for innovation in structural mechanics remains vast, promising a future of even more advanced and resilient engineering solutions.