Curved Beam

Modelling a curved beam subjected to out-of-plane loading and evaluating its deflection: Create a quarter-circle beam with a rectangular cross-section Apply loading by means of an out-of-plane force Neglecting self-weight in the defined load case Determine the maximum deflection of the curved beam Keywords: curved beam arc line rectangular cross-section nodal load deflection

PythonC#

from dlubal.api import rfem, common
from math import inf, pi, cos, sin

# -------------------------------------------------------
# This example demonstrates how to modelling a
# quarter-circle beam with a rectangular cross-section
# which is loaded by means of an out-of-plane force.
# While neglecting self-weight, the total deflection
# of the curved beam is retrieved.
# -------------------------------------------------------


# Editable parameters (SI units)
BEAM_RADIUS = 1
MATERIAL = 'S235'
CSS_WIDTH = 0.025
CSS_HEIGHT = 0.050
LOAD_FZ = 1000


def define_structure() -> list:
    """Define and return a list of structural objects."""

    return [
        rfem.structure_core.Material(
            no=1,
            name=MATERIAL,
        ),

        # Cross-Sections
        rfem.structure_core.CrossSection(
            no=1,
            material=1,
            type=rfem.structure_core.CrossSection.TYPE_PARAMETRIC_MASSIVE_I,
            b=CSS_WIDTH,
            h=CSS_HEIGHT,
        ),

        # Nodes
        rfem.structure_core.Node(
            no=1,
            coordinate_1=0.0,
            coordinate_2=0.0,
        ),
        rfem.structure_core.Node(
            no=2,
            coordinate_1=BEAM_RADIUS,
            coordinate_2=BEAM_RADIUS,
        ),

        # Lines
        rfem.structure_core.Line(
            no=1,
            type=rfem.structure_core.Line.TYPE_ARC,
            definition_nodes=[1, 2],
            arc_control_point=common.Vector3d(
                x=BEAM_RADIUS + BEAM_RADIUS*cos(3*pi/4),
                y=BEAM_RADIUS*sin(3*pi/4),
                z=0
            ),
        ),

        # Members
        rfem.structure_core.Member(
            no=1,
            line=1,
            cross_section_start=1,
            rotation_specification_type=rfem.structure_core.Member.ROTATION_SPECIFICATION_TYPE_INSIDE,
        ),

        # Nodal Supports
        rfem.types_for_nodes.NodalSupport(
            no=1,
            specific_direction_enabled=True,
            nodes=[1],
            spring=common.Vector3d(x=inf, y=inf, z=inf),
            rotational_restraint=common.Vector3d(x=inf, y=inf, z=inf),
            axes_sequence=rfem.types_for_nodes.NodalSupport.AXES_SEQUENCE_ZYX,
            rotated_about_angle_1=pi/2,
        ),
    ]

def define_loading() -> list:
    """Define and return a list of loading objects."""

    return [

        # Static Analysis Settings
        rfem.loading.StaticAnalysisSettings(
            no=1,
        ),

        # Load Cases
        rfem.loading.LoadCase(
            no=1,
            static_analysis_settings=1,
            self_weight_active=False,
        ),

        # Nodal Loads | LC1
        rfem.loads.NodalLoad(
            no=1,
            load_type=rfem.loads.NodalLoad.LOAD_TYPE_COMPONENTS,
            nodes=[2],
            components_force=common.Vector3d(x=0, y=0, z=LOAD_FZ),
            load_case=1,
        ),
    ]

# Connect to the RFEM application
with rfem.Application() as rfem_app:

    app_info = rfem_app.get_application_info()
    print(f"\nApplication Info:\n{app_info}")

    # Modelling
    rfem_app.create_model(name="curved_beam")
    rfem_app.delete_all_objects()
    rfem_app.create_object_list(define_structure() + define_loading())

    # Calculation
    calculation_info = rfem_app.calculate_all(
        skip_warnings=True
    )
    print(f"\nCalculation Info:\n{calculation_info}")

    # Results
    member_deformation_df = rfem_app.get_results(
        results_type=rfem.results.STATIC_ANALYSIS_MEMBERS_LOCAL_DEFORMATIONS
    ).data

    # Maximum deflection
    max_u_z = member_deformation_df["u_z"].abs().max()
    print(f"Max |u_z|: {max_u_z}")