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3.20 Determine the displacements and Green-Lagrange strain components for the deformed configuration shown in Fig. P3.20. The undeformed configuration is shown in dashed lines. Use the suggested form of the deformation mapping, as implied by the deformed configuration. X₂, X₂ -a-B x₂ =q₂X₁ + a₂X², x₂ = b₂ X₁ + b₂ X₂, x₂=X₂. x₁ =q₂X₁ + a₂ X² X₁, X₂ Fig. P3.20

3.20 Determine the displacements and Green-Lagrange strain components for the deformed configuration shown in Fig. P3.20. The undeformed configuration is shown in dashed lines. Use the suggested form of the deformation mapping, as implied by the deformed configuration. X₂, X₂ -a-B x₂ =q₂X₁ + a₂X², x₂ = b₂ X₁ + b₂ X₂, x₂=X₂. x₁ =q₂X₁ + a₂ X² X₁, X₂ Fig. P3.20

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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### Problem Statement: **3.20** Determine the displacements and Green–Lagrange strain components for the deformed configuration shown in Fig. P3.20. The undeformed configuration is shown in dashed lines. Use the suggested form of the deformation mapping, as implied by the deformed configuration. ### Figure Description: The diagram in Fig. P3.20 illustrates a deformation mapping process. It shows both the undeformed configuration (dashed lines) and the deformed configuration (solid lines) on a Cartesian coordinate system. Key aspects of the diagram include: - **Coordinate Axes:** - \( x_1, X_1 \) and \( x_2, X_2 \) are shown as horizontal and vertical axes on the plane, respectively. - \( x_3, X_3 \) is indicated, representing an axis perpendicular to the \( x_1, x_2 \) plane. - **Points and Lines:** - Points \( A \), \( B \), \( C \), and \( D \) are marked on the plane, defining the boundaries of both undeformed (dashed) and deformed (solid) shapes. - The distance \( a \) represents the length from \( A \) to \( B \). - The height \( b \) represents the length from \( A \) to \( D \). - **Deformation Variables:** - \( x_1 = a_1 X_1 + a_4 X_2^2 \) - \( x_2 = b_1 X_1 + b_2 X_2 \) - \( x_3 = X_3 \) These equations describe the mapping of the initial undeformed coordinates \( X_1, X_2, X_3 \) to the deformed coordinates \( x_1, x_2, x_3 \). ### Additional Elements: - The deformation is suggested to consider the transformation outlined by the equations, implying elongation and curvature as shown by the diagram's solid lines. - The dimensions \( e \) on both the horizontal and vertical axes signify the amount of displacement in each direction. This transcribed content would be suitable for inclusion in an educational context, explaining the process of determining displacements and strains due to deformation.
Transcribed Image Text:### Problem Statement: **3.20** Determine the displacements and Green–Lagrange strain components for the deformed configuration shown in Fig. P3.20. The undeformed configuration is shown in dashed lines. Use the suggested form of the deformation mapping, as implied by the deformed configuration. ### Figure Description: The diagram in Fig. P3.20 illustrates a deformation mapping process. It shows both the undeformed configuration (dashed lines) and the deformed configuration (solid lines) on a Cartesian coordinate system. Key aspects of the diagram include: - **Coordinate Axes:** - \( x_1, X_1 \) and \( x_2, X_2 \) are shown as horizontal and vertical axes on the plane, respectively. - \( x_3, X_3 \) is indicated, representing an axis perpendicular to the \( x_1, x_2 \) plane. - **Points and Lines:** - Points \( A \), \( B \), \( C \), and \( D \) are marked on the plane, defining the boundaries of both undeformed (dashed) and deformed (solid) shapes. - The distance \( a \) represents the length from \( A \) to \( B \). - The height \( b \) represents the length from \( A \) to \( D \). - **Deformation Variables:** - \( x_1 = a_1 X_1 + a_4 X_2^2 \) - \( x_2 = b_1 X_1 + b_2 X_2 \) - \( x_3 = X_3 \) These equations describe the mapping of the initial undeformed coordinates \( X_1, X_2, X_3 \) to the deformed coordinates \( x_1, x_2, x_3 \). ### Additional Elements: - The deformation is suggested to consider the transformation outlined by the equations, implying elongation and curvature as shown by the diagram's solid lines. - The dimensions \( e \) on both the horizontal and vertical axes signify the amount of displacement in each direction. This transcribed content would be suitable for inclusion in an educational context, explaining the process of determining displacements and strains due to deformation.
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